What is the derivative of sin(5x+sin^2(5x)) ?

The derivative of sin(5x+sin^2(5x)) is cos(5x)*5+5sin(10x)

What is the first derivative of sin(5x+sin^2(5x)) ?

The first derivative of sin(5x+sin^2(5x)) is cos(5x)*5+5sin(10x)

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\frac{d}{d x} (sin (5 x) + sin^{2} (5 x))

cos (5 x) \cdot 5 + 5 sin (10 x)

Solution steps

\frac{d}{d x} (sin (5 x) + sin^{2} (5 x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sin (5 x)) + \frac{d}{d x} (sin^{2} (5 x))

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

\frac{d}{d x} (sin^{2} (5 x)) = 5 sin (10 x)

= cos (5 x) \cdot 5 + 5 sin (10 x)

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\int_{- \infty}^{1} \frac{1}{x ^{2} + 1} d x

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What is the derivative of sin(5x+sin^2(5x)) ?
The derivative of sin(5x+sin^2(5x)) is cos(5x)*5+5sin(10x)
What is the first derivative of sin(5x+sin^2(5x)) ?
The first derivative of sin(5x+sin^2(5x)) is cos(5x)*5+5sin(10x)