What is the derivative of (x^3+2x-7(3+x-x^2)) ?

The derivative of (x^3+2x-7(3+x-x^2)) is -5x^4+4x^3+3x^2+18x-1

What is the first derivative of (x^3+2x-7(3+x-x^2)) ?

The first derivative of (x^3+2x-7(3+x-x^2)) is -5x^4+4x^3+3x^2+18x-1

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\frac{d}{d x} ((x^{3} + 2 x - 7) (3 + x - x^{2}))

- 5 x^{4} + 4 x^{3} + 3 x^{2} + 18 x - 1

Solution steps

\frac{d}{d x} ((x^{3} + 2 x - 7) (3 + x - x^{2}))

Apply the Product Rule:

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

f = x^{3} + 2 x - 7, g = 3 + x - x^{2}

= \frac{d}{d x} (x^{3} + 2 x - 7) (3 + x - x^{2}) + \frac{d}{d x} (3 + x - x^{2}) (x^{3} + 2 x - 7)

\frac{d}{d x} (x^{3} + 2 x - 7) = 3 x^{2} + 2

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

= (3 x^{2} + 2) (3 + x - x^{2}) + (- 2 x + 1) (x^{3} + 2 x - 7)

Simplify

(3 x^{2} + 2) (3 + x - x^{2}) + (- 2 x + 1) (x^{3} + 2 x - 7) : - 5 x^{4} + 4 x^{3} + 3 x^{2} + 18 x - 1

= - 5 x^{4} + 4 x^{3} + 3 x^{2} + 18 x - 1

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

\frac{d y}{d x} - 2 x y = 8 x

x \to 1 - lim (∣ x - 1 ∣)

\int \frac{4 x ^{3}}{e ^{2 x^{2}}} d x

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

What is the derivative of (x^3+2x-7(3+x-x^2)) ?
The derivative of (x^3+2x-7(3+x-x^2)) is -5x^4+4x^3+3x^2+18x-1
What is the first derivative of (x^3+2x-7(3+x-x^2)) ?
The first derivative of (x^3+2x-7(3+x-x^2)) is -5x^4+4x^3+3x^2+18x-1