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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of x^{1/3}(x^{4/3}+9)^8

\int x^{\frac{1}{3}} (x^{\frac{4}{3}} + 9)^{8} d x

integral of sin^2(2x)cos^5(2x)

\int sin^{2} (2 x) cos^{5} (2 x) d x

derivative of 1/(s^2+1)derivative of

\frac{1}{s ^{2} + 1}

join 1/3 cot(9x)join

\frac{1}{3} cot (9 x)

limit as x approaches-2-of f(x)

x \to - 2 - lim (f (x))

Frequently Asked Questions (FAQ)

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