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Popular >

derivative of x^2sqrt(x^2-9)

Solution

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

Solution

\frac{3 x ^{3} - 18 x}{x ^{2} - 9}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x x^{2} - 9 + \frac{x}{x ^{2} - 9} x^{2} : \frac{3 x ^{3} - 18 x}{x ^{2} - 9}

= \frac{3 x ^{3} - 18 x}{x ^{2} - 9}

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limit as x approaches 12 of (x^3)/3

x \to 12 lim (\frac{x ^{3}}{3})

(\partial)/(\partial y)(x+y-320)

\frac{\partial}{\partial y} (x + y - 320)

(\partial)/(\partial x)(x^4+y^3)

\frac{\partial}{\partial x} (x^{4} + y^{3})

taylor 1/(1+x),0 taylor

\frac{1}{1 + x}, 0

sum from n=1 to infinity of (-9^n)/(n^4)

n = 1 \sum \infty \frac{- 9 ^{n}}{n ^{4}}

Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(x^2-9) ?
The derivative of x^2sqrt(x^2-9) is (3x^3-18x)/(sqrt(x^2-9))
What is the first derivative of x^2sqrt(x^2-9) ?
The first derivative of x^2sqrt(x^2-9) is (3x^3-18x)/(sqrt(x^2-9))