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

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

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

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

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\frac{d}{d x} (x^{3} \cdot 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}

\int 9 x^{- 1} d x

\int \frac{1}{( 2 x - 3 ) ^{2}} d x

f (x) = \frac{3}{( x + 5 ) ^{2}}, at x = 1

x \to 3 lim (\frac{∣ x + 7 ∣}{x - 3})

f (t) = 3 t - t^{2}, (0, 0)

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