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Popular >

derivative of xcos(x^3)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Graph

Popular Examples

derivative of (5x^6/2+(12)/(7x^5)-x)

\frac{d}{d x} (\frac{5 x ^{6}}{2} + \frac{12}{7 x ^{5}} - x)

integral of (4x)/(x-8)

\int \frac{4 x}{x - 8} d x

limit as x approaches 0 of arcsin(1+2x)

x \to 0 lim (arcsin (1 + 2 x))

integral from 1 to 5 of 7/(x^2)

\int_{1}^{5} \frac{7}{x ^{2}} d x

derivative of (5x+8^3)

\frac{d}{d x} ((5 x + 8)^{3})

Frequently Asked Questions (FAQ)

What is the derivative of xcos(x^3) ?
The derivative of xcos(x^3) is cos(x^3)-3x^3sin(x^3)
What is the first derivative of xcos(x^3) ?
The first derivative of xcos(x^3) is cos(x^3)-3x^3sin(x^3)