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Popular >

derivative of e^{cos(x^3})

Solution

\frac{d}{d x} (e^{c o s (x^{3})})

Solution

- 3 e^{c o s (x^{3})} x^{2} sin (x^{3})

Solution steps

\frac{d}{d x} (e^{c o s (x^{3})})

Apply the chain rule:

e^{c o s (x^{3})} \frac{d}{d x} (cos (x^{3}))

= e^{c o s (x^{3})} \frac{d}{d x} (cos (x^{3}))

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

= e^{c o s (x^{3})} (- sin (x^{3}) \cdot 3 x^{2})

Simplify

= - 3 e^{c o s (x^{3})} x^{2} sin (x^{3})

Popular Examples

integral of (9x^4)/2 sin(1.3x)

\int \frac{9 x ^{4}}{2} sin (1.3 x) d x

derivative of 10(e^{x/(20}+e^{-x/(20)}))

\frac{d}{d x} (10 (e^{\frac{x}{20}} + e^{- \frac{x}{20}}))

limit as x approaches 2 of 3x-6

x \to 2 lim (3 x - 6)

integral of 7cos(sqrt(5x))

\int 7 cos (5 x) d x

limit as x approaches 1 of (ln(x))/(4x-x^2-3)

x \to 1 lim (\frac{ln ( x )}{4 x - x ^{2} - 3})

Frequently Asked Questions (FAQ)

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