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Popular >

derivative of ((x-1(2x+3)+7)^5)

Solution

\frac{d}{d x} (((x - 1) (2 x + 3) + 7)^{5})

Solution

5 (2 x^{2} + x + 4)^{4} (4 x + 1)

Solution steps

\frac{d}{d x} (((x - 1) (2 x + 3) + 7)^{5})

Simplify

((x - 1) (2 x + 3) + 7)^{5} : (2 x^{2} + x + 4)^{5}

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

Apply the chain rule:

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

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

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

= 5 (2 x^{2} + x + 4)^{4} (4 x + 1)

Graph

Popular Examples

derivative of ax^2e^{-2x}

\frac{d}{d x} (a x^{2} e^{- 2 x})

integral of (3^x)/(4^x)

\int \frac{3 ^{x}}{4 ^{x}} d x

laplacetransform 1/2 e^{-4t}-1/2 e^{-6t}laplace transform

\frac{1}{2} e^{- 4 t} - \frac{1}{2} e^{- 6 t}

limit as x approaches 0-of sin(x)

x \to 0 - lim (sin (x))

x^2y^{''}+2xy^'-30y=0,y(1)=-5,y^'(1)=-6

x^{2} y^{^{''}} + 2 x y^{^{'}} - 30 y = 0, y (1) = - 5, y^{^{'}} (1) = - 6

Frequently Asked Questions (FAQ)

What is the derivative of ((x-1(2x+3)+7)^5) ?
The derivative of ((x-1(2x+3)+7)^5) is 5(2x^2+x+4)^4(4x+1)
What is the first derivative of ((x-1(2x+3)+7)^5) ?
The first derivative of ((x-1(2x+3)+7)^5) is 5(2x^2+x+4)^4(4x+1)