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Popular >

derivative of (8x+5(x^2-3x))

Solution

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

Solution

24 x^{2} - 38 x - 15

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (8 x + 5) = 8

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

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

Simplify

8 (x^{2} - 3 x) + (2 x - 3) (8 x + 5) : 24 x^{2} - 38 x - 15

= 24 x^{2} - 38 x - 15

Popular Examples

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

integral from 1 to 6 of 2/(x^3)

\int_{1}^{6} \frac{2}{x ^{3}} d x

tangent of 6-4x^2 tangent of

6 - 4 x^{2}

(dy)/(dx)-2/3 xy= 1/3 y^3

\frac{d y}{d x} - \frac{2}{3} x y = \frac{1}{3} y^{3}

integral of 4x^4(27+x^5)^{1/3}

\int 4 x^{4} (27 + x^{5})^{\frac{1}{3}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (8x+5(x^2-3x)) ?
The derivative of (8x+5(x^2-3x)) is 24x^2-38x-15
What is the first derivative of (8x+5(x^2-3x)) ?
The first derivative of (8x+5(x^2-3x)) is 24x^2-38x-15