What is the derivative of (x^3+1(x^2-3x)) ?

The derivative of (x^3+1(x^2-3x)) is 5x^4-12x^3+2x-3

What is the first derivative of (x^3+1(x^2-3x)) ?

The first derivative of (x^3+1(x^2-3x)) is 5x^4-12x^3+2x-3

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

5 x^{4} - 12 x^{3} + 2 x - 3

Solution steps

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

Apply the Product Rule:

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

f = x^{3} + 1, g = x^{2} - 3 x

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

\frac{d}{d x} (x^{3} + 1) = 3 x^{2}

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

= 3 x^{2} (x^{2} - 3 x) + (2 x - 3) (x^{3} + 1)

Simplify

3 x^{2} (x^{2} - 3 x) + (2 x - 3) (x^{3} + 1) : 5 x^{4} - 12 x^{3} + 2 x - 3

= 5 x^{4} - 12 x^{3} + 2 x - 3

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

\int_{0}^{4} 2^{x} d x

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

\int e^{t} d t

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 0, y^{^{'}} (0) = 1

What is the derivative of (x^3+1(x^2-3x)) ?
The derivative of (x^3+1(x^2-3x)) is 5x^4-12x^3+2x-3
What is the first derivative of (x^3+1(x^2-3x)) ?
The first derivative of (x^3+1(x^2-3x)) is 5x^4-12x^3+2x-3