What is the derivative of (x^2+5x-6(x^3+5x-8)) ?

The derivative of (x^2+5x-6(x^3+5x-8)) is 5x^4+20x^3-3x^2+34x-70

What is the first derivative of (x^2+5x-6(x^3+5x-8)) ?

The first derivative of (x^2+5x-6(x^3+5x-8)) is 5x^4+20x^3-3x^2+34x-70

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\frac{d}{d x} ((x^{2} + 5 x - 6) (x^{3} + 5 x - 8))

5 x^{4} + 20 x^{3} - 3 x^{2} + 34 x - 70

Solution steps

\frac{d}{d x} ((x^{2} + 5 x - 6) (x^{3} + 5 x - 8))

Apply the Product Rule:

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

f = x^{2} + 5 x - 6, g = x^{3} + 5 x - 8

= \frac{d}{d x} (x^{2} + 5 x - 6) (x^{3} + 5 x - 8) + \frac{d}{d x} (x^{3} + 5 x - 8) (x^{2} + 5 x - 6)

\frac{d}{d x} (x^{2} + 5 x - 6) = 2 x + 5

\frac{d}{d x} (x^{3} + 5 x - 8) = 3 x^{2} + 5

= (2 x + 5) (x^{3} + 5 x - 8) + (3 x^{2} + 5) (x^{2} + 5 x - 6)

Simplify

(2 x + 5) (x^{3} + 5 x - 8) + (3 x^{2} + 5) (x^{2} + 5 x - 6) : 5 x^{4} + 20 x^{3} - 3 x^{2} + 34 x - 70

= 5 x^{4} + 20 x^{3} - 3 x^{2} + 34 x - 70

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

f (x) = 3 + e^{x}

\int tan (7 x) d x

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\int 2 x cos (5 x) d x

What is the derivative of (x^2+5x-6(x^3+5x-8)) ?
The derivative of (x^2+5x-6(x^3+5x-8)) is 5x^4+20x^3-3x^2+34x-70
What is the first derivative of (x^2+5x-6(x^3+5x-8)) ?
The first derivative of (x^2+5x-6(x^3+5x-8)) is 5x^4+20x^3-3x^2+34x-70