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Popular Calculus >

derivative of y=e^{4cos(sqrt(x))}

Solution

derivative of

y = e^{4 c o s (x)}

Solution

- \frac{2 e ^{4 c o s (x)} sin ( x )}{x}

Solution steps

\frac{d}{d x} (e^{4 c o s (x)})

Apply the chain rule:

e^{4 c o s (x)} \frac{d}{d x} (4 cos (x))

= e^{4 c o s (x)} \frac{d}{d x} (4 cos (x))

\frac{d}{d x} (4 cos (x)) = - \frac{2 sin ( x )}{x}

= e^{4 c o s (x)} (- \frac{2 sin ( x )}{x})

Simplify

e^{4 c o s (x)} (- \frac{2 sin ( x )}{x}) : - \frac{2 e ^{4 c o s (x)} sin ( x )}{x}

= - \frac{2 e ^{4 c o s (x)} sin ( x )}{x}

Graph

Popular Examples

limit as h approaches 0 of sin(1/h)

h \to 0 lim (sin (\frac{1}{h}))

integral of 2sin^3(2x)cos^3(2x)

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

limit as x approaches+10 of x

x \to + 10 lim (x)

(dy)/(dx)=x^6y^{-7},y(0)=4

\frac{d y}{d x} = x^{6} y^{- 7}, y (0) = 4

derivative of arcsin(cos(x))

\frac{d}{d x} (arcsin (cos (x)))

Frequently Asked Questions (FAQ)

What is the derivative of y=e^{4cos(sqrt(x))} ?
The derivative of y=e^{4cos(sqrt(x))} is -(2e^{4cos(sqrt(x))}sin(sqrt(x)))/(sqrt(x))
What is the first derivative of y=e^{4cos(sqrt(x))} ?
The first derivative of y=e^{4cos(sqrt(x))} is -(2e^{4cos(sqrt(x))}sin(sqrt(x)))/(sqrt(x))