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Popular >

derivative of x^2sqrt(7x-5)

Solution

\frac{d}{d x} (x^{2} 7 x - 5)

Solution

\frac{35 x ^{2} - 20 x}{2 7 x - 5}

Solution steps

\frac{d}{d x} (x^{2} 7 x - 5)

Apply the Product Rule:

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

f = x^{2}, g = 7 x - 5

= \frac{d}{d x} (x^{2}) 7 x - 5 + \frac{d}{d x} (7 x - 5) x^{2}

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

\frac{d}{d x} (7 x - 5) = \frac{7}{2 7 x - 5}

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

Simplify

2 x 7 x - 5 + \frac{7}{2 7 x - 5} x^{2} : \frac{35 x ^{2} - 20 x}{2 7 x - 5}

= \frac{35 x ^{2} - 20 x}{2 7 x - 5}

Popular Examples

derivative of |x-9|

\frac{d}{d x} (∣ x - 9 ∣)

y^{''}-2y^'+37y=0

y^{^{''}} - 2 y^{^{'}} + 37 y = 0

limit as x approaches 0+of (x^x-1)/x

x \to 0 + lim (\frac{x ^{x} - 1}{x})

(dy)/(dx)=sec(x)+ytan(x)

\frac{d y}{d x} = sec (x) + y tan (x)

integral of 2/9 x^{-1/9}

\int \frac{2}{9} x^{- \frac{1}{9}} d x

Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(7x-5) ?
The derivative of x^2sqrt(7x-5) is (35x^2-20x)/(2sqrt(7x-5))
What is the first derivative of x^2sqrt(7x-5) ?
The first derivative of x^2sqrt(7x-5) is (35x^2-20x)/(2sqrt(7x-5))