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Popular >

derivative of y=(4x+3)(2x^2+7x-1)

Solution

derivative of

y = (4 x + 3) (2 x^{2} + 7 x - 1)

Solution

24 x^{2} + 68 x + 17

Solution steps

\frac{d}{d x} ((4 x + 3) (2 x^{2} + 7 x - 1))

Apply the Product Rule:

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

f = 4 x + 3, g = 2 x^{2} + 7 x - 1

= \frac{d}{d x} (4 x + 3) (2 x^{2} + 7 x - 1) + \frac{d}{d x} (2 x^{2} + 7 x - 1) (4 x + 3)

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

\frac{d}{d x} (2 x^{2} + 7 x - 1) = 4 x + 7

= 4 (2 x^{2} + 7 x - 1) + (4 x + 7) (4 x + 3)

Simplify

4 (2 x^{2} + 7 x - 1) + (4 x + 7) (4 x + 3) : 24 x^{2} + 68 x + 17

= 24 x^{2} + 68 x + 17

Popular Examples

integral from 0 to 1/7 of xarcsin(7x)

\int_{0}^{\frac{1}{7}} x arcsin (7 x) d x

(2dy)/(dx)-4xy=8x,y(0)=15

\frac{2 d y}{d x} - 4 x y = 8 x, y (0) = 15

derivative of ln((1+x^2/(1-x^2)))

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

integral of 1/(sqrt(t^2-10t+29))

\int \frac{1}{t ^{2} - 10 t + 29} d t

(d^2y)/(dx^2)=((dy)/(dx))^2

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

Frequently Asked Questions (FAQ)

What is the derivative of y=(4x+3)(2x^2+7x-1) ?
The derivative of y=(4x+3)(2x^2+7x-1) is 24x^2+68x+17
What is the first derivative of y=(4x+3)(2x^2+7x-1) ?
The first derivative of y=(4x+3)(2x^2+7x-1) is 24x^2+68x+17