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Rigoberto Stevens
11 April, 00:23
Find f' (x) for f (x) = cos^2 (5x^3).
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Cody Gaines
11 April, 00:44
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d/dx cos^2 (5x^3)
= d/dx [cos (5x^3) ]^2
= 2[cos (5x^3) ]
= - 2[cos (5x^3) ] * sin (5x^3)
= - 2[cos (5x^3) ] * sin (5x^3) * 15x^2
= - 30[cos (5x^3) ] * sin (5x^3) * x^2
Explanation:
d/dx x^n = nx^ (n - 1)
d/dx cos x = - sin x
Chain rule:
d/dx f (g ( ... w (x))) = f' (g ( ... w (x))) * g' ( ... w (x)) * ... * w' (x)
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Patience Payne
11 April, 01:08
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Step-by-step explanation:
f (x) = cos² (5x³)
f (x) = (cos (5x³)) ²
Use chain rule to find the derivative:
f' (x) = 2 cos (5x³) * - sin (5x³) * 15x²
f' (x) = - 30x² sin (5x³) cos (5x³)
If desired, use double angle formula to simplify:
f' (x) = - 15x² sin (10x³)
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