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Popular >

derivative of f(x)=x^4sin(4x)

Solution

derivative of

f (x) = x^{4} sin (4 x)

Solution

4 x^{3} sin (4 x) + cos (4 x) \cdot 4 x^{4}

Solution steps

\frac{d}{d x} (x^{4} sin (4 x))

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (sin (4 x)) = cos (4 x) \cdot 4

= 4 x^{3} sin (4 x) + cos (4 x) \cdot 4 x^{4}

Popular Examples

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\int_{1}^{2} 1

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n = 0 \sum \infty \frac{π ^{n}}{e ^{n}}

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t \to 1 lim (7 e^{t} - 3)

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\int_{1}^{e} ln (6 x) d x

area y=(x^2+4)/(3x-x^2),(1,2)area

y = \frac{x ^{2} + 4}{3 x - x ^{2}}, (1, 2)

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^4sin(4x) ?
The derivative of f(x)=x^4sin(4x) is 4x^3sin(4x)+cos(4x)*4x^4
What is the first derivative of f(x)=x^4sin(4x) ?
The first derivative of f(x)=x^4sin(4x) is 4x^3sin(4x)+cos(4x)*4x^4