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Popular >

derivative of x^2sqrt(10x-7)

Solution

\frac{d}{d x} (x^{2} 10 x - 7)

Solution

\frac{25 x ^{2} - 14 x}{10 x - 7}

Solution steps

\frac{d}{d x} (x^{2} 10 x - 7)

Apply the Product Rule:

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

f = x^{2}, g = 10 x - 7

= \frac{d}{d x} (x^{2}) 10 x - 7 + \frac{d}{d x} (10 x - 7) x^{2}

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

\frac{d}{d x} (10 x - 7) = \frac{5}{10 x - 7}

= 2 x 10 x - 7 + \frac{5}{10 x - 7} x^{2}

Simplify

2 x 10 x - 7 + \frac{5}{10 x - 7} x^{2} : \frac{25 x ^{2} - 14 x}{10 x - 7}

= \frac{25 x ^{2} - 14 x}{10 x - 7}

Popular Examples

derivative of f(x)=(x-1)e^x derivative of

f (x) = (x - 1) e^{x}

limit as x approaches 1-of 2^{1/(x-2)}

x \to 1 - lim (2^{\frac{1}{x - 2}})

integral of (sqrt(9-x^2))/(x^2)

\int \frac{9 - x ^{2}}{x ^{2}} d x

tangent of f(x)=2x^2+8x,\at x=2 tangent of

f (x) = 2 x^{2} + 8 x, at x = 2

integral of (2X^2-7X-2)/(X^3-X)

\int \frac{2 X ^{2} - 7 X - 2}{X ^{3} - X} d X

Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(10x-7) ?
The derivative of x^2sqrt(10x-7) is (25x^2-14x)/(sqrt(10x-7))
What is the first derivative of x^2sqrt(10x-7) ?
The first derivative of x^2sqrt(10x-7) is (25x^2-14x)/(sqrt(10x-7))