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Popular Calculus >

derivative of sin(2x^2*e^{-x})

Solution

\frac{d}{d x} (sin (2 x^{2} \cdot e^{- x}))

Solution

cos (2 x^{2} e^{- x}) \cdot 2 (2 e^{- x} x - e^{- x} x^{2})

Solution steps

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

Apply the chain rule:

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

= cos (2 x^{2} e^{- x}) \frac{d}{d x} (2 x^{2} e^{- x})

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

= cos (2 x^{2} e^{- x}) \cdot 2 (2 e^{- x} x - e^{- x} x^{2})

Graph

Popular Examples

tangent of f(x)=(x-2)(2x+3),\at x=0

t an g e n t f (x) = (x - 2) (2 x + 3), at x = 0

integral of (x-5)*sin(x)

\int (x - 5) \cdot sin (x) d x

integral of (sin(x)tan(x))/(9+sec^2(x))

\int \frac{sin ( x ) tan ( x )}{9 + sec ^{2} ( x )} d x

t^2y^{''}+21ty^'+100y=0

t^{2} y^{^{''}} + 21 t y^{^{'}} + 100 y = 0

limit as x approaches 2 of 5a+ax

x \to 2 lim (5 a + a x)

Frequently Asked Questions (FAQ)

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