What is the derivative of f(x)=x^4sin(2x) ?

The derivative of f(x)=x^4sin(2x) is 4x^3sin(2x)+cos(2x)*2x^4

What is the first derivative of f(x)=x^4sin(2x) ?

The first derivative of f(x)=x^4sin(2x) is 4x^3sin(2x)+cos(2x)*2x^4

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derivative of

f (x) = x^{4} sin (2 x)

4 x^{3} sin (2 x) + cos (2 x) \cdot 2 x^{4}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 4 x^{3} sin (2 x) + cos (2 x) \cdot 2 x^{4}

What is the derivative of f(x)=x^4sin(2x) ?
The derivative of f(x)=x^4sin(2x) is 4x^3sin(2x)+cos(2x)*2x^4
What is the first derivative of f(x)=x^4sin(2x) ?
The first derivative of f(x)=x^4sin(2x) is 4x^3sin(2x)+cos(2x)*2x^4