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Popular >

derivative of (x^3-9)sqrt(x)

Solution

derivative of

(x^{3} - 9) x

Solution

\frac{7 x ^{3} - 9}{2 x}

Solution steps

\frac{d}{d x} ((x^{3} - 9) x)

Apply the Product Rule:

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

f = x^{3} - 9, g = x

= \frac{d}{d x} (x^{3} - 9) x + \frac{d}{d x} (x) (x^{3} - 9)

\frac{d}{d x} (x^{3} - 9) = 3 x^{2}

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

= 3 x^{2} x + \frac{1}{2 x} (x^{3} - 9)

Simplify

3 x^{2} x + \frac{1}{2 x} (x^{3} - 9) : \frac{7 x ^{3} - 9}{2 x}

= \frac{7 x ^{3} - 9}{2 x}

Popular Examples

derivative of (2w^3-w)/w derivative of

\frac{2 w ^{3} - w}{w}

integral of t(t^2+1)^5

\int t (t^{2} + 1)^{5} d t

sum from n=0 to infinity of (n-1)/(n^2)

n = 0 \sum \infty \frac{n - 1}{n ^{2}}

integral of 1+e^t

\int 1 + e^{t} d t

y^{''}+0.1y^'+0.0004y=0

y^{^{''}} + 0.1 y^{^{'}} + 0.0004 y = 0

Frequently Asked Questions (FAQ)

What is the derivative of (x^3-9)sqrt(x) ?
The derivative of (x^3-9)sqrt(x) is (7x^3-9)/(2sqrt(x))
What is the first derivative of (x^3-9)sqrt(x) ?
The first derivative of (x^3-9)sqrt(x) is (7x^3-9)/(2sqrt(x))