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Popular >

derivative of x^2e^xsin(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

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f (x) = \frac{x + 9}{x ^{2} - 7 x + 1}

integral of x*sin(x^2)

\int x \cdot sin (x^{2}) d x

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\int_{- 2}^{2} x^{2} 1 + 4 x^{2} d x

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\int 5 sin (6 π x) d x

simplify ln((5x+2)(3x-4)^2)simplify

ln ((5 x + 2) (3 x - 4)^{2})

Frequently Asked Questions (FAQ)

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