What is the derivative of x(2x-3)^{1/2} ?

The derivative of x(2x-3)^{1/2} is (3x-3)/((2x-3)^{1/2)}

What is the first derivative of x(2x-3)^{1/2} ?

The first derivative of x(2x-3)^{1/2} is (3x-3)/((2x-3)^{1/2)}

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derivative of

x (2 x - 3)^{\frac{1}{2}}

\frac{3 x - 3}{( 2 x - 3 ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (x (2 x - 3)^{\frac{1}{2}})

Apply the Product Rule:

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

f = x, g = (2 x - 3)^{\frac{1}{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

y = \frac{3}{2}, y = \frac{1}{1 - x ^{2}}

ln (\frac{e ^{2 x} ( x ^{2} + 3 )}{x + 2})

- x^{2} + 3 x - 2

\frac{d}{d x} (x e^{- b x})

\int (5 t^{2} + 3 t) d t

What is the derivative of x(2x-3)^{1/2} ?
The derivative of x(2x-3)^{1/2} is (3x-3)/((2x-3)^{1/2)}
What is the first derivative of x(2x-3)^{1/2} ?
The first derivative of x(2x-3)^{1/2} is (3x-3)/((2x-3)^{1/2)}