What is the derivative of x*(3*x-4)^{0.5} ?

The derivative of x*(3*x-4)^{0.5} is (4.5x-4)/((3x-4)^{1/2)}

What is the first derivative of x*(3*x-4)^{0.5} ?

The first derivative of x*(3*x-4)^{0.5} is (4.5x-4)/((3x-4)^{1/2)}

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derivative of

x \cdot (3 \cdot x - 4)^{0.5}

\frac{4.5 x - 4}{( 3 x - 4 ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (x (3 x - 4)^{0.5})

Apply the Product Rule:

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

f = x, g = (3 x - 4)^{0.5}

= \frac{d x}{d x} (3 x - 4)^{0.5} + \frac{d}{d x} ((3 x - 4)^{0.5}) x

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

\frac{d}{d x} ((3 x - 4)^{0.5}) = \frac{1.5}{( 3 x - 4 ) ^{\frac{1}{2}}}

= 1 \cdot (3 x - 4)^{0.5} + \frac{1.5}{( 3 x - 4 ) ^{\frac{1}{2}}} x

Simplify

1 \cdot (3 x - 4)^{\frac{1}{2}} + \frac{1.5}{( 3 x - 4 ) ^{\frac{1}{2}}} x : \frac{4.5 x - 4}{( 3 x - 4 ) ^{\frac{1}{2}}}

= \frac{4.5 x - 4}{( 3 x - 4 ) ^{\frac{1}{2}}}

\frac{\partial}{\partial y} (x z - 5 x^{2} y^{3} z^{4})

\frac{d}{d x} (\frac{- 10 x + 4}{3 x - 8})

y = x^{2} + x

\int (x + y) d x

\frac{d y}{d x}, (3 x y + 7)^{2} = 6 y

What is the derivative of x*(3*x-4)^{0.5} ?
The derivative of x*(3*x-4)^{0.5} is (4.5x-4)/((3x-4)^{1/2)}
What is the first derivative of x*(3*x-4)^{0.5} ?
The first derivative of x*(3*x-4)^{0.5} is (4.5x-4)/((3x-4)^{1/2)}