What is the derivative of (4x^2-1/2 x(9x+8)) ?

The derivative of (4x^2-1/2 x(9x+8)) is 108x^2+55x-4

What is the first derivative of (4x^2-1/2 x(9x+8)) ?

The first derivative of (4x^2-1/2 x(9x+8)) is 108x^2+55x-4

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\frac{d}{d x} ((4 x^{2} - \frac{1}{2} x) (9 x + 8))

108 x^{2} + 55 x - 4

Solution steps

\frac{d}{d x} ((4 x^{2} - \frac{1}{2} x) (9 x + 8))

Simplify

(4 x^{2} - \frac{1}{2} x) (9 x + 8) : (4 x^{2} - \frac{x}{2}) (9 x + 8)

= \frac{d}{d x} ((4 x^{2} - \frac{x}{2}) (9 x + 8))

Apply the Product Rule:

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

f = 4 x^{2} - \frac{x}{2}, g = 9 x + 8

= \frac{d}{d x} (4 x^{2} - \frac{x}{2}) (9 x + 8) + \frac{d}{d x} (9 x + 8) (4 x^{2} - \frac{x}{2})

\frac{d}{d x} (4 x^{2} - \frac{x}{2}) = 8 x - \frac{1}{2}

\frac{d}{d x} (9 x + 8) = 9

= (8 x - \frac{1}{2}) (9 x + 8) + 9 (4 x^{2} - \frac{x}{2})

Simplify

(8 x - \frac{1}{2}) (9 x + 8) + 9 (4 x^{2} - \frac{x}{2}) : 108 x^{2} + 55 x - 4

= 108 x^{2} + 55 x - 4

\frac{d}{d x} (3 e^{4 x})

2 y^{^{'}} = 3 x y + 1

x \to 1 lim ((x^{2} - 2 x + 1) cos (e^{\frac{1}{x - 1}}))

x \to \infty lim ([2, x])

\int (sin^{2} (x) - cos^{2} (x)) d x

What is the derivative of (4x^2-1/2 x(9x+8)) ?
The derivative of (4x^2-1/2 x(9x+8)) is 108x^2+55x-4
What is the first derivative of (4x^2-1/2 x(9x+8)) ?
The first derivative of (4x^2-1/2 x(9x+8)) is 108x^2+55x-4