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Popular >

derivative of x^2sqrt(6x-7)

Solution

\frac{d}{d x} (x^{2} 6 x - 7)

Solution

\frac{15 x ^{2} - 14 x}{6 x - 7}

Solution steps

\frac{d}{d x} (x^{2} 6 x - 7)

Apply the Product Rule:

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

f = x^{2}, g = 6 x - 7

= \frac{d}{d x} (x^{2}) 6 x - 7 + \frac{d}{d x} (6 x - 7) x^{2}

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

\frac{d}{d x} (6 x - 7) = \frac{3}{6 x - 7}

= 2 x 6 x - 7 + \frac{3}{6 x - 7} x^{2}

Simplify

2 x 6 x - 7 + \frac{3}{6 x - 7} x^{2} : \frac{15 x ^{2} - 14 x}{6 x - 7}

= \frac{15 x ^{2} - 14 x}{6 x - 7}

Popular Examples

derivative of ln(5x^2+7y^2)derivative of

ln (5 x^{2} + 7 y^{2})

tangent of f(x)=1+5e^x,\at x=1 tangent of

f (x) = 1 + 5 e^{x}, at x = 1

integral of (x+2)/(x^2(x-5))

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

xy+y^2+x^2-x^2y^'=0

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

integral of sin(105x)sin(45x)

\int sin (105 x) sin (45 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(6x-7) ?
The derivative of x^2sqrt(6x-7) is (15x^2-14x)/(sqrt(6x-7))
What is the first derivative of x^2sqrt(6x-7) ?
The first derivative of x^2sqrt(6x-7) is (15x^2-14x)/(sqrt(6x-7))