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Mathematics
Skye Lawrence
12 November, 08:34
Derive (sinx) / (1+tanx)
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Hayley Atkins
12 November, 09:10
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You use the quotient rule for derivatives since you are dividing.
We will use F (x) for sinx and G (x) for (1+tanx), and H' (x) for the final answer.
So H' (x) = (F' (x) G (x) - F (x) G' (x)) / (G (x)) ^ (2))
The derivative of sinx is cosx so F' (x) = cosx
The derivative of 1+tanx is sec^ (2) x, just like the derivative of tangent (because the derivative of a constant is 0, and by the addition rule for derivatives you would add the derivatives). 0 + sec^ (2) x is sec^ (2) x. So G' (x) is sec^ (2) x.
So with this information just plug F, F', G, and G' into the H' (x) = (F' (x) G (x) - F (x) G' (x)) / (G (x)) ^ (2)) equation and solve.
H' (x) = (cosx) (1+tanx) - (sinx) (sec^ (2) x) / ((1+tanx) ^ (2))
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