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Popular >

derivative of y=(4x^2+5)(2x-3)

Solution

derivative of

y = (4 x^{2} + 5) (2 x - 3)

Solution

24 x^{2} - 24 x + 10

Solution steps

\frac{d}{d x} ((4 x^{2} + 5) (2 x - 3))

Apply the Product Rule:

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

f = 4 x^{2} + 5, g = 2 x - 3

= \frac{d}{d x} (4 x^{2} + 5) (2 x - 3) + \frac{d}{d x} (2 x - 3) (4 x^{2} + 5)

\frac{d}{d x} (4 x^{2} + 5) = 8 x

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

= 8 x (2 x - 3) + 2 (4 x^{2} + 5)

Simplify

8 x (2 x - 3) + 2 (4 x^{2} + 5) : 24 x^{2} - 24 x + 10

= 24 x^{2} - 24 x + 10

Popular Examples

\frac{d}{d j} (3 i - 4 j)

(dy)/(dx)+3tan(3x)y=-5cos(3x)

\frac{d y}{d x} + 3 tan (3 x) y = - 5 cos (3 x)

limit as x approaches 0 of x

x \to 0 lim (x)

sum from n=0 to infinity of (-1^n)/(n+2)

n = 0 \sum \infty \frac{- 1 ^{n}}{n + 2}

\frac{d h}{d t} = - h^{2}

Frequently Asked Questions (FAQ)

What is the derivative of y=(4x^2+5)(2x-3) ?
The derivative of y=(4x^2+5)(2x-3) is 24x^2-24x+10
What is the first derivative of y=(4x^2+5)(2x-3) ?
The first derivative of y=(4x^2+5)(2x-3) is 24x^2-24x+10