What is the derivative of ln(cos(sin(e^{x^3}))) ?

The derivative of ln(cos(sin(e^{x^3}))) is -3e^{x^3}x^2cos(e^{x^3})tan(sin(e^{x^3}))

What is the first derivative of ln(cos(sin(e^{x^3}))) ?

The first derivative of ln(cos(sin(e^{x^3}))) is -3e^{x^3}x^2cos(e^{x^3})tan(sin(e^{x^3}))

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\frac{d}{d x} (ln (cos (sin (e^{x^{3}}))))

- 3 e^{x^{3}} x^{2} cos (e^{x^{3}}) tan (sin (e^{x^{3}}))

Solution steps

\frac{d}{d x} (ln (cos (sin (e^{x^{3}}))))

Apply the chain rule:

\frac{1}{cos ( sin ( e ^{x^{3}} ) )} \frac{d}{d x} (cos (sin (e^{x^{3}})))

= \frac{1}{cos ( sin ( e ^{x^{3}} ) )} \frac{d}{d x} (cos (sin (e^{x^{3}})))

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

= \frac{1}{cos ( sin ( e ^{x^{3}} ) )} (- sin (sin (e^{x^{3}})) cos (e^{x^{3}}) e^{x^{3}} \cdot 3 x^{2})

Simplify

\frac{1}{cos ( sin ( e ^{x^{3}} ) )} (- sin (sin (e^{x^{3}})) cos (e^{x^{3}}) e^{x^{3}} \cdot 3 x^{2}) : - 3 e^{x^{3}} x^{2} cos (e^{x^{3}}) tan (sin (e^{x^{3}}))

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

What is the derivative of ln(cos(sin(e^{x^3}))) ?
The derivative of ln(cos(sin(e^{x^3}))) is -3e^{x^3}x^2cos(e^{x^3})tan(sin(e^{x^3}))
What is the first derivative of ln(cos(sin(e^{x^3}))) ?
The first derivative of ln(cos(sin(e^{x^3}))) is -3e^{x^3}x^2cos(e^{x^3})tan(sin(e^{x^3}))