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))

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derivative of

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

\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}

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))