What is the derivative of (x^2+2x-1*(2x^2-3x+6)) ?

The derivative of (x^2+2x-1*(2x^2-3x+6)) is 8x^3+3x^2-4x+15

What is the first derivative of (x^2+2x-1*(2x^2-3x+6)) ?

The first derivative of (x^2+2x-1*(2x^2-3x+6)) is 8x^3+3x^2-4x+15

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\frac{d}{d x} ((x^{2} + 2 x - 1) \cdot (2 x^{2} - 3 x + 6))

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

Solution steps

\frac{d}{d x} ((x^{2} + 2 x - 1) (2 x^{2} - 3 x + 6))

Apply the Product Rule:

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

f = x^{2} + 2 x - 1, g = 2 x^{2} - 3 x + 6

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

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

\frac{d}{d x} (2 x^{2} - 3 x + 6) = 4 x - 3

= (2 x + 2) (2 x^{2} - 3 x + 6) + (4 x - 3) (x^{2} + 2 x - 1)

Simplify

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

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

\int 2 e^{- x} d x

h \to 0 lim (\frac{1}{h + 1})

x^{2} + 2 x y - y^{2} + x = 6, (2, 4)

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

\int_{0}^{1} 8^{2 x} d x

What is the derivative of (x^2+2x-1*(2x^2-3x+6)) ?
The derivative of (x^2+2x-1*(2x^2-3x+6)) is 8x^3+3x^2-4x+15
What is the first derivative of (x^2+2x-1*(2x^2-3x+6)) ?
The first derivative of (x^2+2x-1*(2x^2-3x+6)) is 8x^3+3x^2-4x+15