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Popular >

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

Solution

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

Solution

\frac{5 x ^{2} - 14 x}{2 x - 7}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (2 x - 7) = \frac{1}{2 x - 7}

= 2 x 2 x - 7 + \frac{1}{2 x - 7} x^{2}

Simplify

2 x 2 x - 7 + \frac{1}{2 x - 7} x^{2} : \frac{5 x ^{2} - 14 x}{2 x - 7}

= \frac{5 x ^{2} - 14 x}{2 x - 7}

Popular Examples

integral of (e^{8x})/(e^{8x)+7}

\int \frac{e ^{8 x}}{e ^{8 x} + 7} d x

integral of 1/(cos^3(x))

\int \frac{1}{cos ^{3} ( x )} d x

limit as x approaches-infinity of x

x \to - \infty lim (x)

derivative of y=x^{11}e^x derivative of

y = x^{11} e^{x}

(\partial)/(\partial x)(-7x^2+7y^2-7)

\frac{\partial}{\partial x} (- 7 x^{2} + 7 y^{2} - 7)

Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(2x-7) ?
The derivative of x^2sqrt(2x-7) is (5x^2-14x)/(sqrt(2x-7))
What is the first derivative of x^2sqrt(2x-7) ?
The first derivative of x^2sqrt(2x-7) is (5x^2-14x)/(sqrt(2x-7))