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Popular >

derivative of x^2sqrt(8x-5)

Solution

\frac{d}{d x} (x^{2} 8 x - 5)

Solution

\frac{20 x ^{2} - 10 x}{8 x - 5}

Solution steps

\frac{d}{d x} (x^{2} 8 x - 5)

Apply the Product Rule:

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

f = x^{2}, g = 8 x - 5

= \frac{d}{d x} (x^{2}) 8 x - 5 + \frac{d}{d x} (8 x - 5) x^{2}

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

\frac{d}{d x} (8 x - 5) = \frac{4}{8 x - 5}

= 2 x 8 x - 5 + \frac{4}{8 x - 5} x^{2}

Simplify

2 x 8 x - 5 + \frac{4}{8 x - 5} x^{2} : \frac{20 x ^{2} - 10 x}{8 x - 5}

= \frac{20 x ^{2} - 10 x}{8 x - 5}

Popular Examples

sum from n=0 to infinity of 4(1/10)^n

n = 0 \sum \infty 4 (\frac{1}{10})^{n}

t^{2} y^{^{'}} + t y = 7

integral of (x^2)/((x^2+4)^{3/2)}

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

derivative of f(x)=(27)/(5e^2)-3/2 derivative of

f (x) = \frac{27}{5 e ^{2}} - \frac{3}{2}

derivative of sqrt(x+1)(16+8x+9x^2)

\frac{d}{d x} (x + 1 (16 + 8 x + 9 x^{2}))

Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(8x-5) ?
The derivative of x^2sqrt(8x-5) is (20x^2-10x)/(sqrt(8x-5))
What is the first derivative of x^2sqrt(8x-5) ?
The first derivative of x^2sqrt(8x-5) is (20x^2-10x)/(sqrt(8x-5))