What is the derivative of x^3sin(7x) ?

The derivative of x^3sin(7x) is 3x^2sin(7x)+cos(7x)*7x^3

What is the first derivative of x^3sin(7x) ?

The first derivative of x^3sin(7x) is 3x^2sin(7x)+cos(7x)*7x^3

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derivative of

x^{3} sin (7 x)

3 x^{2} sin (7 x) + cos (7 x) \cdot 7 x^{3}

Solution steps

\frac{d}{d x} (x^{3} sin (7 x))

Apply the Product Rule:

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

f = x^{3}, g = sin (7 x)

= \frac{d}{d x} (x^{3}) sin (7 x) + \frac{d}{d x} (sin (7 x)) x^{3}

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

\frac{d}{d x} (sin (7 x)) = cos (7 x) \cdot 7

= 3 x^{2} sin (7 x) + cos (7 x) \cdot 7 x^{3}

What is the derivative of x^3sin(7x) ?
The derivative of x^3sin(7x) is 3x^2sin(7x)+cos(7x)*7x^3
What is the first derivative of x^3sin(7x) ?
The first derivative of x^3sin(7x) is 3x^2sin(7x)+cos(7x)*7x^3