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Popular Calculus >

derivative of (6x+5)(x^2-3x)

Solution

derivative of

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

Solution

18 x^{2} - 26 x - 15

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

6 (x^{2} - 3 x) + (2 x - 3) (6 x + 5) : 18 x^{2} - 26 x - 15

= 18 x^{2} - 26 x - 15

Graph

Popular Examples

integral of 9x^5

\int 9 x^{5} d x

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\int sin (r^{2}) d r

integral of cos(2pit)

\int cos (2 π t) d t

(\partial)/(\partial u)(sqrt(u^5+v^7))

\frac{\partial}{\partial u} (u^{5} + v^{7})

(\partial)/(\partial x)(sqrt(y^2+16))

\frac{\partial}{\partial x} (y^{2} + 16)

Frequently Asked Questions (FAQ)

What is the derivative of (6x+5)(x^2-3x) ?
The derivative of (6x+5)(x^2-3x) is 18x^2-26x-15
What is the first derivative of (6x+5)(x^2-3x) ?
The first derivative of (6x+5)(x^2-3x) is 18x^2-26x-15