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Popular >

derivative of f(x)=(2x-3)*sqrt(x)

Solution

derivative of

f (x) = (2 x - 3) \cdot x

Solution

\frac{6 x - 3}{2 x}

Solution steps

\frac{d}{d x} ((2 x - 3) x)

Apply the Product Rule:

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

f = 2 x - 3, g = x

= \frac{d}{d x} (2 x - 3) x + \frac{d}{d x} (x) (2 x - 3)

\frac{d}{d x} (2 x - 3) = 2

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

= 2 x + \frac{1}{2 x} (2 x - 3)

Simplify

2 x + \frac{1}{2 x} (2 x - 3) : \frac{6 x - 3}{2 x}

= \frac{6 x - 3}{2 x}

Popular Examples

integral of 1-2/(x^2)

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

integral of (e^x)/(sqrt(e^x+1)+1)

\int \frac{e ^{x}}{e ^{x} + 1 + 1} d x

integral of ((2x+3)^2)/(sqrt(x))

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

derivative of 2sin(x)

\frac{d}{d x} (2 sin (x))

tangent of 2/(1-t),\at t=-2 tangent of

\frac{2}{1 - t}, at t = - 2

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(2x-3)*sqrt(x) ?
The derivative of f(x)=(2x-3)*sqrt(x) is (6x-3)/(2sqrt(x))
What is the first derivative of f(x)=(2x-3)*sqrt(x) ?
The first derivative of f(x)=(2x-3)*sqrt(x) is (6x-3)/(2sqrt(x))