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Popular >

derivative of xsqrt(x^2+9)

Solution

derivative of

x x^{2} + 9

Solution

\frac{2 x ^{2} + 9}{x ^{2} + 9}

Solution steps

\frac{d}{d x} (x x^{2} + 9)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{2} + 9

= \frac{d x}{d x} x^{2} + 9 + \frac{d}{d x} (x^{2} + 9) x

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} + 9) = \frac{x}{x ^{2} + 9}

= 1 \cdot x^{2} + 9 + \frac{x}{x ^{2} + 9} x

Simplify

1 \cdot x^{2} + 9 + \frac{x}{x ^{2} + 9} x : \frac{2 x ^{2} + 9}{x ^{2} + 9}

= \frac{2 x ^{2} + 9}{x ^{2} + 9}

Popular Examples

derivative of x^4-32x^2

\frac{d}{d x} (x^{4} - 32 x^{2})

y^{''}+2y^'+10y=0,y(0)=3,y^'(0)=-1

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = 3, y^{^{'}} (0) = - 1

limit as x approaches 2 of 4x^2-8x

x \to 2 lim (4 x^{2} - 8 x)

derivative of (e^{6x}/x)

\frac{d}{d x} (\frac{e ^{6 x}}{x})

limit as x approaches 3 of x+3

x \to 3 lim (x + 3)

Frequently Asked Questions (FAQ)

What is the derivative of xsqrt(x^2+9) ?
The derivative of xsqrt(x^2+9) is (2x^2+9)/(sqrt(x^2+9))
What is the first derivative of xsqrt(x^2+9) ?
The first derivative of xsqrt(x^2+9) is (2x^2+9)/(sqrt(x^2+9))