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Popular >

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

Solution

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

Solution

24 x^{2} - 40 x + 6

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (4 x^{2} + 3) = 8 x

\frac{d}{d x} (2 x - 5) = 2

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

Simplify

8 x (2 x - 5) + 2 (4 x^{2} + 3) : 24 x^{2} - 40 x + 6

= 24 x^{2} - 40 x + 6

Popular Examples

derivative of tan^4((1-x/(1+x)))

\frac{d}{d x} (tan^{4} (\frac{1 - x}{1 + x}))

(dy)/(dt)=-0.4y+6.2e^{-0.73t},y(0)=0

\frac{d y}{d t} = - 0.4 y + 6.2 e^{- 0.73 t}, y (0) = 0

(dy)/(dx)=((y^2-1))/((x^2-1)),y(2)=2

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

limit as x approaches infinity of 5x

x \to \infty lim (5 x)

integral from 0 to 6 of 7000te^{-0.1t}

\int_{0}^{6} 7000 t e^{- 0.1 t} d t

Frequently Asked Questions (FAQ)

What is the derivative of (4x^2+3(2x-5)) ?
The derivative of (4x^2+3(2x-5)) is 24x^2-40x+6
What is the first derivative of (4x^2+3(2x-5)) ?
The first derivative of (4x^2+3(2x-5)) is 24x^2-40x+6