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

The derivative of (x^2-6(x^3+x^2+x+2)) is 5x^4+4x^3-15x^2-8x-6

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

The first derivative of (x^2-6(x^3+x^2+x+2)) is 5x^4+4x^3-15x^2-8x-6

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

5 x^{4} + 4 x^{3} - 15 x^{2} - 8 x - 6

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 2 x (x^{3} + x^{2} + x + 2) + (3 x^{2} + 2 x + 1) (x^{2} - 6)

Simplify

2 x (x^{3} + x^{2} + x + 2) + (3 x^{2} + 2 x + 1) (x^{2} - 6) : 5 x^{4} + 4 x^{3} - 15 x^{2} - 8 x - 6

= 5 x^{4} + 4 x^{3} - 15 x^{2} - 8 x - 6

\int 2 (x - 6)^{3} d x

2 x^{2} cos (x) cot (x)

\int \frac{25}{25 + e ^{x}} d x

x y^{^{'}} + y = - 3 x y^{2}, y (1) = - 4

f (x) = ln^{4} (x)

What is the derivative of (x^2-6(x^3+x^2+x+2)) ?
The derivative of (x^2-6(x^3+x^2+x+2)) is 5x^4+4x^3-15x^2-8x-6
What is the first derivative of (x^2-6(x^3+x^2+x+2)) ?
The first derivative of (x^2-6(x^3+x^2+x+2)) is 5x^4+4x^3-15x^2-8x-6