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Popular >

derivative of xsin(x^3)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot sin (x^{3}) + cos (x^{3}) \cdot 3 x^{2} x

Simplify

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

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

Popular Examples

integral from-1 to 5 of (y^2-5)-4y

\int_{- 1}^{5} (y^{2} - 5) - 4 y d y

integral from 0 to 2 of 20000e^{0.03x}

\int_{0}^{2} 20000 e^{0.03 x} d x

sum from k=1 to infinity of k*2^{-k}

k = 1 \sum \infty k \cdot 2^{- k}

limit as h approaches 0 of-8p-4h-7

h \to 0 lim (- 8 p - 4 h - 7)

limit as x approaches 0 of (e^x+x)^{8/x}

x \to 0 lim ((e^{x} + x)^{\frac{8}{x}})

Frequently Asked Questions (FAQ)

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