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Popular >

derivative of x^2sqrt(4x-9)

Solution

\frac{d}{d x} (x^{2} 4 x - 9)

Solution

\frac{10 x ^{2} - 18 x}{4 x - 9}

Solution steps

\frac{d}{d x} (x^{2} 4 x - 9)

Apply the Product Rule:

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

f = x^{2}, g = 4 x - 9

= \frac{d}{d x} (x^{2}) 4 x - 9 + \frac{d}{d x} (4 x - 9) x^{2}

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

\frac{d}{d x} (4 x - 9) = \frac{2}{4 x - 9}

= 2 x 4 x - 9 + \frac{2}{4 x - 9} x^{2}

Simplify

2 x 4 x - 9 + \frac{2}{4 x - 9} x^{2} : \frac{10 x ^{2} - 18 x}{4 x - 9}

= \frac{10 x ^{2} - 18 x}{4 x - 9}

Graph

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\int (- 3 (\frac{9 x ^{2}}{2}) - 4 x^{3}) d x

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\int 30 e^{0.5 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(4x-9) ?
The derivative of x^2sqrt(4x-9) is (10x^2-18x)/(sqrt(4x-9))
What is the first derivative of x^2sqrt(4x-9) ?
The first derivative of x^2sqrt(4x-9) is (10x^2-18x)/(sqrt(4x-9))