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Popular >

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

Solution

derivative of

x (x - 9)^{2}

Solution

\frac{5 x ^{2} - 54 x + 81}{2 x}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

= \frac{1}{2 x} (x - 9)^{2} + 2 (x - 9) x

Simplify

\frac{1}{2 x} (x - 9)^{2} + 2 (x - 9) x : \frac{5 x ^{2} - 54 x + 81}{2 x}

= \frac{5 x ^{2} - 54 x + 81}{2 x}

Popular Examples

integral from 2 to 4 of 5x^2

\int_{2}^{4} 5 x^{2} d x

tangent of f(x)=4-x^2,\at x=-4 tangent of

f (x) = 4 - x^{2}, at x = - 4

integral of (10)/(sqrt(x))+10sqrt(x)

\int \frac{10}{x} + 10 x d x

limit as x approaches-2+of (|x+2|)/(x+2)

x \to - 2 + lim (\frac{∣ x + 2 ∣}{x + 2})

integral of (x+11)/(x^2+16x+68)

\int \frac{x + 11}{x ^{2} + 16 x + 68} d x

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)(x-9)^2 ?
The derivative of sqrt(x)(x-9)^2 is (5x^2-54x+81)/(2sqrt(x))
What is the first derivative of sqrt(x)(x-9)^2 ?
The first derivative of sqrt(x)(x-9)^2 is (5x^2-54x+81)/(2sqrt(x))