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Popular >

derivative of x^2sin(sqrt(x))

Solution

derivative of

x^{2} sin (x)

Solution

2 x sin (x) + \frac{x ^{\frac{3}{2}} cos ( x )}{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\frac{cos ( x )}{2 x} x^{2} = \frac{x ^{\frac{3}{2}} cos ( x )}{2}

= 2 x sin (x) + \frac{x ^{\frac{3}{2}} cos ( x )}{2}

Popular Examples

integral of (arctan(3x))/(1+9x^2)

\int \frac{arctan ( 3 x )}{1 + 9 x ^{2}} d x

integral from 0 to pi of sin(3x)sin(5x)

\int_{0}^{π} sin (3 x) sin (5 x) d x

derivative of (4x^2+4x+6/(sqrt(x)))

\frac{d}{d x} (\frac{4 x ^{2} + 4 x + 6}{x})

integral from 3 to 6 of (x^2-2x)

\int_{3}^{6} (x^{2} - 2 x) d x

integral of 1/((x^2-4)^2)

\int \frac{1}{( x ^{2} - 4 ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of x^2sin(sqrt(x)) ?
The derivative of x^2sin(sqrt(x)) is 2xsin(sqrt(x))+(x^{3/2}cos(sqrt(x)))/2
What is the first derivative of x^2sin(sqrt(x)) ?
The first derivative of x^2sin(sqrt(x)) is 2xsin(sqrt(x))+(x^{3/2}cos(sqrt(x)))/2