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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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\int_{- π}^{0} sin (x) + x d x

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\int_{0}^{π} 2 cos^{2} (\frac{π}{2}) d x

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\int \frac{2}{7} x^{2} + 1 d x

Frequently Asked Questions (FAQ)

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