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

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

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

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

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

- sin (sin (5 x^{2})) cos (5 x^{2}) \cdot 10 x

Solution steps

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

Apply the chain rule:

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

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

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

= - sin (sin (5 x^{2})) cos (5 x^{2}) \cdot 10 x

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