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Popular >

derivative of e^xcos(x^2)

Solution

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

Solution

e^{x} cos (x^{2}) - 2 e^{x} x sin (x^{2})

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = cos (x^{2})

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

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

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

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

Simplify

= e^{x} cos (x^{2}) - 2 e^{x} x sin (x^{2})

Popular Examples

limit as y approaches-1 of-y^5-3y^4

y \to - 1 lim (- y^{5} - 3 y^{4})

tangent of f(x)=e^{2x},(0,1)tangent of

f (x) = e^{2 x}, (0, 1)

sum from n=1 to infinity of (-1)^nn^{-1}

n = 1 \sum \infty (- 1)^{n} n^{- 1}

y^{''}+5y^'=e^{-t},y(0)=0,y^'(0)=0

y^{^{''}} + 5 y^{^{'}} = e^{- t}, y (0) = 0, y^{^{'}} (0) = 0

y^'=8x+y,y(0)=6

y^{^{'}} = 8 x + y, y (0) = 6

Frequently Asked Questions (FAQ)

What is the derivative of e^xcos(x^2) ?
The derivative of e^xcos(x^2) is e^xcos(x^2)-2e^xxsin(x^2)
What is the first derivative of e^xcos(x^2) ?
The first derivative of e^xcos(x^2) is e^xcos(x^2)-2e^xxsin(x^2)