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Popular Calculus >

derivative of xcos(1-e^x)

Solution

derivative of

x cos (1 - e^{x})

Solution

cos (1 - e^{x}) + e^{x} x sin (1 - e^{x})

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cos (1 - e^{x})

= \frac{d x}{d x} cos (1 - e^{x}) + \frac{d}{d x} (cos (1 - e^{x})) x

\frac{d x}{d x} = 1

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

= 1 \cdot cos (1 - e^{x}) + e^{x} sin (1 - e^{x}) x

Simplify

= cos (1 - e^{x}) + e^{x} x sin (1 - e^{x})

Graph

Popular Examples

integral of (7/(x^5)+4x+3)

\int (\frac{7}{x ^{5}} + 4 x + 3) d x

derivative of ln(xsqrt(x))

d er i v a t i v e ln (x x)

tangent of 18sqrt(x)-3x

t an g e n t 18 x - 3 x

(dy)/(dt)+4y=2e^{-3t}

\frac{d y}{d t} + 4 y = 2 e^{- 3 t}

derivative of x^{52}-1/(x^2)

\frac{d}{d x} (x^{52} - \frac{1}{x ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of xcos(1-e^x) ?
The derivative of xcos(1-e^x) is cos(1-e^x)+e^xxsin(1-e^x)
What is the first derivative of xcos(1-e^x) ?
The first derivative of xcos(1-e^x) is cos(1-e^x)+e^xxsin(1-e^x)