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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Graph

Popular Examples

integral of x^2-4x+3

\int x^{2} - 4 x + 3 d x

derivative of 1/2 x^2sqrt(49-x^2)derivative of

\frac{1}{2} x^{2} 49 - x^{2}

integral of cos^5(x)sin(2x)

\int cos^{5} (x) sin (2 x) d x

(\partial)/(\partial x)(x^2-2xy+6y^2+x-5y)

\frac{\partial}{\partial x} (x^{2} - 2 x y + 6 y^{2} + x - 5 y)

integral of y^5

\int y^{5} d y

Frequently Asked Questions (FAQ)

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