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Popular >

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

Solution

derivative of

e^{c o s (x)} + cos (e^{x})

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (e^{c o s (x)}) = - e^{c o s (x)} sin (x)

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

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

Popular Examples

limit as x approaches 1 of sqrt(1-x^2)

x \to 1 lim (1 - x^{2})

derivative of (x^3+5/x)

\frac{d}{d x} (\frac{x ^{3} + 5}{x})

derivative of ,xe^y+y^2x-x^3,\at (1,0)

\frac{d}{d x} (, x e^{y} + y^{2} x - x^{3}, at (1, 0))

sum from n=0 to infinity of 1/(1+n^2)

n = 0 \sum \infty \frac{1}{1 + n ^{2}}

integral of x^2arcsin(x)

\int x^{2} arcsin (x) d x

Frequently Asked Questions (FAQ)

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