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Popular Calculus >

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}

Graph

Popular Examples

derivative of 2sin(x)

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

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

t an g e n t \frac{2}{1 - t}, at t = - 2

taylor f(x)=30^3-3x^2+12x-74

t a y l or f (x) = 3 0^{3} - 3 x^{2} + 12 x - 74

derivative of 6e^{-2x}

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

limit as x approaches-2+of (x+3)/(x+2)

x \to - 2 + lim (\frac{x + 3}{x + 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))