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

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

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

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

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derivative of

f (x) = x^{3} sin (x)

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\frac{d}{d x} (\frac{x ^{2} - 6 x + 1}{( x ^{2} - 1 ) ^{2}})

\int cos (x) (5 + 5 sin^{2} (x)) d x

\int x^{2} - 9 x + 3 d x

f (x) = x x, (9, 27)

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