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Popular >

derivative of f(x)=sqrt(5x^2+3x+8)

Solution

derivative of

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

Solution

\frac{10 x + 3}{2 5 x ^{2} + 3 x + 8}

Solution steps

\frac{d}{d x} (5 x^{2} + 3 x + 8)

Apply the chain rule:

\frac{1}{2 5 x ^{2} + 3 x + 8} \frac{d}{d x} (5 x^{2} + 3 x + 8)

= \frac{1}{2 5 x ^{2} + 3 x + 8} \frac{d}{d x} (5 x^{2} + 3 x + 8)

\frac{d}{d x} (5 x^{2} + 3 x + 8) = 10 x + 3

= \frac{1}{2 5 x ^{2} + 3 x + 8} (10 x + 3)

Simplify

\frac{1}{2 5 x ^{2} + 3 x + 8} (10 x + 3) : \frac{10 x + 3}{2 5 x ^{2} + 3 x + 8}

= \frac{10 x + 3}{2 5 x ^{2} + 3 x + 8}

Popular Examples

derivative of 7/(8x^3)derivative of

\frac{7}{8 x ^{3}}

derivative of e^{-x/5}

\frac{d}{d x} (e^{- \frac{x}{5}})

tangent of f(x)= 1/((1+x^2)),\at x=1 tangent of

f (x) = \frac{1}{( 1 + x ^{2} )}, at x = 1

(dy)/(dx)+y=(1-e^{-2x})/(e^x-e^{-x)}

\frac{d y}{d x} + y = \frac{1 - e ^{- 2 x}}{e ^{x} - e ^{- x}}

integral of x(4x-3)^{10}

\int x (4 x - 3)^{10} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(5x^2+3x+8) ?
The derivative of f(x)=sqrt(5x^2+3x+8) is (10x+3)/(2sqrt(5x^2+3x+8))
What is the first derivative of f(x)=sqrt(5x^2+3x+8) ?
The first derivative of f(x)=sqrt(5x^2+3x+8) is (10x+3)/(2sqrt(5x^2+3x+8))