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Popular >

derivative of 5x^4sin^3(2x)

Solution

\frac{d}{d x} (5 x^{4} sin^{3} (2 x))

Solution

5 (4 x^{3} sin^{3} (2 x) + 6 sin^{2} (2 x) cos (2 x) x^{4})

Solution steps

\frac{d}{d x} (5 x^{4} sin^{3} (2 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (x^{4} sin^{3} (2 x))

Apply the Product Rule:

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

f = x^{4}, g = sin^{3} (2 x)

= 5 (\frac{d}{d x} (x^{4}) sin^{3} (2 x) + \frac{d}{d x} (sin^{3} (2 x)) x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (sin^{3} (2 x)) = 6 sin^{2} (2 x) cos (2 x)

= 5 (4 x^{3} sin^{3} (2 x) + 6 sin^{2} (2 x) cos (2 x) x^{4})

Popular Examples

derivative of (5x^6+4x^5+3x^4/(6x^2))

\frac{d}{d x} (\frac{5 x ^{6} + 4 x ^{5} + 3 x ^{4}}{6 x ^{2}})

derivative of (x^2-2e^x)/(x+3e^x)derivative of

\frac{x ^{2} - 2 e ^{x}}{x + 3 e ^{x}}

derivative of (x^3+1/(sqrt(x^3-1)))

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

derivative of f(x)=sec^2(0)derivative of

f (x) = sec^{2} (0)

integral of 1/((3x-1)^4)

\int \frac{1}{( 3 x - 1 ) ^{4}} d x

Frequently Asked Questions (FAQ)

What is the derivative of 5x^4sin^3(2x) ?
The derivative of 5x^4sin^3(2x) is 5(4x^3sin^3(2x)+6sin^2(2x)cos(2x)x^4)
What is the first derivative of 5x^4sin^3(2x) ?
The first derivative of 5x^4sin^3(2x) is 5(4x^3sin^3(2x)+6sin^2(2x)cos(2x)x^4)