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Popular >

derivative of x^3sin(xcos(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

(x^5+y^2)dx-xydy=0

(x^{5} + y^{2}) d x - x y d y = 0

limit as x approaches 7 of 6x+|x-7|

x \to 7 lim (6 x + ∣ x - 7 ∣)

limit as x approaches-5 of x^2-10

x \to - 5 lim (x^{2} - 10)

derivative of (8x^3/3)

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

integral of (tan(θ)-1)^2

\int (tan (θ) - 1)^{2} d θ

Frequently Asked Questions (FAQ)

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