What is the derivative of sin(cos(x^2+3x)) ?

The derivative of sin(cos(x^2+3x)) is -cos(cos(x^2+3x))sin(x^2+3x)(2x+3)

What is the first derivative of sin(cos(x^2+3x)) ?

The first derivative of sin(cos(x^2+3x)) is -cos(cos(x^2+3x))sin(x^2+3x)(2x+3)

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\frac{d}{d x} (sin (cos (x^{2} + 3 x)))

- cos (cos (x^{2} + 3 x)) sin (x^{2} + 3 x) (2 x + 3)

Solution steps

\frac{d}{d x} (sin (cos (x^{2} + 3 x)))

Apply the chain rule:

cos (cos (x^{2} + 3 x)) \frac{d}{d x} (cos (x^{2} + 3 x))

= cos (cos (x^{2} + 3 x)) \frac{d}{d x} (cos (x^{2} + 3 x))

\frac{d}{d x} (cos (x^{2} + 3 x)) = - sin (x^{2} + 3 x) (2 x + 3)

= cos (cos (x^{2} + 3 x)) (- sin (x^{2} + 3 x) (2 x + 3))

Simplify

= - cos (cos (x^{2} + 3 x)) sin (x^{2} + 3 x) (2 x + 3)

What is the derivative of sin(cos(x^2+3x)) ?
The derivative of sin(cos(x^2+3x)) is -cos(cos(x^2+3x))sin(x^2+3x)(2x+3)
What is the first derivative of sin(cos(x^2+3x)) ?
The first derivative of sin(cos(x^2+3x)) is -cos(cos(x^2+3x))sin(x^2+3x)(2x+3)