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Popular >

derivative of x^2sin(x^3)

Solution

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

Popular Examples

derivative of 1/(xx)

\frac{d}{d x} (\frac{1}{xx})

derivative of 564+x(36x^{0.6}-107)

\frac{d}{d x} (564 + x (36 x^{0.6} - 107))

limit as x approaches-1-of x/((x+1)^3)

x \to - 1 - lim (\frac{x}{( x + 1 ) ^{3}})

integral of sqrt(1+4r^2)

\int 1 + 4 r^{2} d r

derivative of 1+sqrt(7x)

\frac{d}{d x} (1 + 7 x)

Frequently Asked Questions (FAQ)

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