Sign In
Ask Question
Mathematics
Konner Frederick
27 July, 08:10
Find dy/dx x^3+y^3=18xy
+1
Answers (
1
)
Dean Turner
27 July, 10:15
0
Differentiate both sides of the equation. d dx (x3 + y3) = d dx (18xy) d dx (x3 + y3) = d dx (18xy) Differentiate the left side of the equation. Tap for fewer steps ... By the Sum Rule, the derivative of x3 + y3 x3 + y3 with respect to xx is d dx [ x3 ] + d dx [ y3 ] d dx [ x3 ] + d dx [ y3 ]. d dx [ x3 ] + d dx [ y3 ] d dx [ x3 ] + d dx [ y3 ] Differentiate using the Power Rule which states that d dx [ xn ] d dx [ xn ] is n x n-1 n x n-1 where n=3 n=3. 3 x2 + d dx [ y3 ] 3 x2 + d dx [ y3 ] Evaluate d dx [ y3 ] d dx [ y3 ]. Tap for more steps ... 3 x2 + 3 y2 d dx [y] 3 x2 + 3 y2 d dx [y] Differentiate the right side of the equation. Tap for fewer steps ... Since 1818 is constant with respect to xx, the derivative of 18xy 18xy with respect to xx is 18 d dx [xy] 18 d dx [xy]. 18 d dx [xy] 18 d dx [xy] Differentiate using the Product Rule which states that d dx [f (x) g (x) ] d dx [f (x) g (x) ] is f (x) d dx [g (x) ] + g (x) d dx [f (x) ] f (x) d dx [g (x) ] + g (x) d dx [f (x) ] where f (x) = x f (x) = x and g (x) = y g (x) = y. 18 (x d dx [y] + y d dx [x]) 18 (x d dx [y] + y d dx [x]) Rewrite d dx [y] d dx [y] as d dx [y] d dx [y]. 18 (x d dx [y] + y d dx [x]) 18 (x d dx [y] + y d dx [x]) Differentiate using the Power Rule which states that d dx [ xn ] d dx [ xn ] is n x n-1 n x n-1 where n=1 n=1. 18 (x d dx [y] + y⋅1) 18 (x d dx [y] + y⋅1) Multiply yy by 11 to get yy. 18 (x d dx [y] + y) 18 (x d dx [y] + y) Simplify. Tap for more steps ... 18x d dx [y] + 18y 18x d dx [y] + 18y Reform the equation by setting the left side equal to the right side. 3 x2 + 3 y2 y'=18xy'+18y 3 x2 + 3 y2 y′=18xy′+18y Since 18xy' 18xy′ contains the variable to solve for, move it to the left side of the equation by subtracting 18xy' 18xy′ from both sides. 3 x2 + 3 y2 y'-18xy'=18y 3 x2 + 3 y2 y′-18xy′=18y Since 3 x2 3 x2 does not contain the variable to solve for, move it to the right side of the equation by subtracting 3 x2 3 x2 from both sides. 3 y2 y'-18xy'=-3 x2 + 18y 3 y2 y′-18xy′=-3 x2 + 18y Factor 3y' 3y′ out of 3 y2 y'-18xy' 3 y2 y′-18xy′. Tap for fewer steps ... Factor 3y' 3y′ out of 3 y2 y' 3 y2 y′. 3y' (y2) - 18xy'=-3 x2 + 18y 3y′ (y2) - 18xy′=-3 x2 + 18y Factor 3y' 3y′ out of - 18xy' - 18xy′. 3y' (y2) + 3y' (-6x) = - 3 x2 + 18y 3y′ (y2) + 3y′ (-6x) = - 3 x2 + 18y Factor 3y' 3y′ out of 3y' y2 + 3y' (-6x) 3y′ y2 + 3y′ (-6x). 3y' (y2 - 6x) = - 3 x2 + 18y 3y′ (y2 - 6x) = - 3 x2 + 18y Divide each term by y2 - 6x y2 - 6x and simplify. Tap for fewer steps ... Divide each term in 3y' (y2 - 6x) = - 3 x2 + 18y 3y′ (y2 - 6x) = - 3 x2 + 18y by y2 - 6x y2 - 6x. 3y' (y2 - 6x) y2 - 6x = - 3 x2 y2 - 6x + 18y y2 - 6x 3y′ (y2 - 6x) y2 - 6x = - 3 x2 y2 - 6x + 18y y2 - 6x Reduce the expression by cancelling the common factors. Tap for more steps ... 3y' = - 3 x2 y2 - 6x + 18y y2 - 6x 3y′ = - 3 x2 y2 - 6x + 18y y2 - 6x Simplify the right side of the equation. Tap for more steps ... 3y' = - 3 (x2 - 6y) y2 - 6x 3y′ = - 3 (x2 - 6y) y2 - 6x Divide each term by 33 and simplify. Tap for fewer steps ... Divide each term in 3y' = - 3 (x2 - 6y) y2 - 6x 3y′ = - 3 (x2 - 6y) y2 - 6x by 33. 3y' 3 = - 3 (x2 - 6y) y2 - 6x 3 3y′ 3 = - 3 (x2 - 6y) y2 - 6x 3 Reduce the expression by cancelling the common factors. Tap for more steps ... y' = - 3 (x2 - 6y) y2 - 6x 3 y′ = - 3 (x2 - 6y) y2 - 6x 3 Simplify the right side of the equation. Tap for more steps ... y' = - x2 - 6y y2 - 6x y′ = - x2 - 6y y2 - 6x Replace y' y′ with dy dx dy dx. dy dx = - x2 - 6y y2 - 6x
Comment
Complaint
Link
Know the Answer?
Answer
Not Sure About the Answer?
Get an answer to your question ✅
“Find dy/dx x^3+y^3=18xy ...”
in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers
You Might be Interested in
The rocket that carried the Curiosity Rover to Mars traveled at a speed of 21,000 miles per hour. What is this speed to the nearest mile per second?
Answers (1)
Which statement is true? a. - 16 23 = - 17 10 b. 15 (-5) > 23 (-12) c. 8 (-7) < - 15 14 d. - 12 (-11) > 5 (-29)
Answers (2)
What is the approximate height of the cylinder? Use 3.14 for pi and if necessary round to the nearest tenth. V = 3.14 ft 3.
Answers (1)
Solving multi-step 3m+6m=36
Answers (2)
Which number would be an element of the set of integers but not an element of the set of whole numbers, 0, - 3, 5, - 1/2?
Answers (1)
New Questions in Mathematics
From least to greatest, what are the possible measures of angle b? round to the nearest whole number.
Answers (1)
If you wanted to know how big the tiger is, which measurments would you use? A. candela, mole B. Kilogram, amphere C. meter, kilogram D. Meter, second
Answers (1)
Classify the number 0. Check all that apply. Real Irrational Rational Integer Whole Natural
Answers (1)
Multistep sandy charges each family that she babysits a flat fee of $10 for the night and an extra $5 per child.
Answers (1)
The circumference of a circular painting is 28.26 feet. What is the diameter of the painting? Use 3.14 for π and do not round your answer.
Answers (1)
Home
»
Mathematics
» Find dy/dx x^3+y^3=18xy
Sign In
Sign Up
Forgot Password?