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Popular >

derivative of x^2*sin(x^3)

Solution

\frac{d}{d x} (x^{2} \cdot sin (x^{3}))

Solution

2 x sin (x^{3}) + 3 x^{4} cos (x^{3})

Solution steps

\frac{d}{d x} (x^{2} sin (x^{3}))

Apply the Product Rule:

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

f = x^{2}, g = sin (x^{3})

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

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

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

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

cos (x^{3}) \cdot 3 x^{2} x^{2} = 3 x^{4} cos (x^{3})

= 2 x sin (x^{3}) + 3 x^{4} cos (x^{3})

Graph

Popular Examples

derivative of (8e^{6x}/(5x+2))

\frac{d}{d x} (\frac{8 e ^{6 x}}{5 x + 2})

integral of sqrt(1/2+(x^4)/4+1/(4x^4))

\int \frac{1}{2} + \frac{x ^{4}}{4} + \frac{1}{4 x ^{4}} d x

y^{''}+4y^'+4y=12t+16

y^{^{''}} + 4 y^{^{'}} + 4 y = 12 t + 16

integral from 0 to 10 of sqrt(1+16x^2)

\int_{0}^{10} 1 + 16 x^{2} d x

integral of (3+x^2)^{3/2}

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

Frequently Asked Questions (FAQ)

What is the derivative of x^2*sin(x^3) ?
The derivative of x^2*sin(x^3) is 2xsin(x^3)+3x^4cos(x^3)
What is the first derivative of x^2*sin(x^3) ?
The first derivative of x^2*sin(x^3) is 2xsin(x^3)+3x^4cos(x^3)