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Popular >

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

Solution

\frac{d}{d x} (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}

Graph

Popular Examples

derivative of (1+cos^2(x))^3 derivative of

(1 + cos^{2} (x))^{3}

(1+x^2)(dy)/(dx)=2xy+1

(1 + x^{2}) \frac{d y}{d x} = 2 x y + 1

derivative of 2x^2sqrt(2-x)

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

derivative of (16/(x^2))

\frac{d}{d x} (\frac{16}{x ^{2}})

(\partial)/(\partial y)(xy^3+x^2)

\frac{\partial}{\partial y} (x y^{3} + x^{2})

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