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Popular >

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

Solution

derivative of

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

Solution

\frac{6 x + 3}{2 3 x ^{2} + 3 x + 3}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2} + 3 x + 3) = 6 x + 3

= \frac{1}{2 3 x ^{2} + 3 x + 3} (6 x + 3)

Simplify

\frac{1}{2 3 x ^{2} + 3 x + 3} (6 x + 3) : \frac{6 x + 3}{2 3 x ^{2} + 3 x + 3}

= \frac{6 x + 3}{2 3 x ^{2} + 3 x + 3}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(3x^2+3x+3) ?
The derivative of f(x)=sqrt(3x^2+3x+3) is (6x+3)/(2sqrt(3x^2+3x+3))
What is the first derivative of f(x)=sqrt(3x^2+3x+3) ?
The first derivative of f(x)=sqrt(3x^2+3x+3) is (6x+3)/(2sqrt(3x^2+3x+3))