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Popular >

derivative of x^2sin(e^x)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

limit as x approaches infinity of sqrt((9x^3+8x-4)/(3-5x+x^3))

x \to \infty lim (\frac{9 x ^{3} + 8 x - 4}{3 - 5 x + x ^{3}})

limit as t approaches infinity of-654e^{-(7t)/(2180)}+654

t \to \infty lim (- 654 e^{- \frac{7 t}{2180}} + 654)

limit as x approaches 10-of 1/(x+10)

x \to 10 - lim (\frac{1}{x + 10})

derivative of (4+x)^2 derivative of

(4 + x)^{2}

derivative of 1/((1-x^2^{3/2)})

\frac{d}{d x} (\frac{1}{( 1 - x ^{2} ) ^{\frac{3}{2}}})

Frequently Asked Questions (FAQ)

What is the derivative of x^2sin(e^x) ?
The derivative of x^2sin(e^x) is 2xsin(e^x)+cos(e^x)e^xx^2
What is the first derivative of x^2sin(e^x) ?
The first derivative of x^2sin(e^x) is 2xsin(e^x)+cos(e^x)e^xx^2