What is the derivative of 8x^{3/2}+6x^{1/2}+4^{-1/2} ?

The derivative of 8x^{3/2}+6x^{1/2}+4^{-1/2} is (3+12x)/(x^{1/2)}

What is the first derivative of 8x^{3/2}+6x^{1/2}+4^{-1/2} ?

The first derivative of 8x^{3/2}+6x^{1/2}+4^{-1/2} is (3+12x)/(x^{1/2)}

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derivative of

8 x^{\frac{3}{2}} + 6 x^{\frac{1}{2}} + 4^{- \frac{1}{2}}

\frac{3 + 12 x}{x ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (8 x^{\frac{3}{2}} + 6 x^{\frac{1}{2}} + 4^{- \frac{1}{2}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (8 x^{\frac{3}{2}}) + \frac{d}{d x} (6 x^{\frac{1}{2}}) + \frac{d}{d x} (4^{- \frac{1}{2}})

\frac{d}{d x} (8 x^{\frac{3}{2}}) = 12 x^{\frac{1}{2}}

\frac{d}{d x} (6 x^{\frac{1}{2}}) = \frac{3}{x ^{\frac{1}{2}}}

\frac{d}{d x} (4^{- \frac{1}{2}}) = 0

= 12 x^{\frac{1}{2}} + \frac{3}{x ^{\frac{1}{2}}} + 0

Simplify

12 x^{\frac{1}{2}} + \frac{3}{x ^{\frac{1}{2}}} + 0 : \frac{3 + 12 x}{x ^{\frac{1}{2}}}

= \frac{3 + 12 x}{x ^{\frac{1}{2}}}

\frac{\partial}{\partial y} (3 x y^{2} e^{4 yz})

x \to 0 + lim (tan^{x} (8 x))

f (x) = x^{2}, (- 1, 1)

\int x cos (2 x^{2} + 7) d x

What is the derivative of 8x^{3/2}+6x^{1/2}+4^{-1/2} ?
The derivative of 8x^{3/2}+6x^{1/2}+4^{-1/2} is (3+12x)/(x^{1/2)}
What is the first derivative of 8x^{3/2}+6x^{1/2}+4^{-1/2} ?
The first derivative of 8x^{3/2}+6x^{1/2}+4^{-1/2} is (3+12x)/(x^{1/2)}