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

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

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

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

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

\frac{1}{6 x ^{\frac{1}{2}}} - \frac{3 x ^{\frac{1}{2}}}{2}

Solution steps

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

Simplify

\frac{1}{3} x^{\frac{1}{2}} - x^{\frac{3}{2}} : \frac{x ^{\frac{1}{2}}}{3} - x^{\frac{3}{2}}

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

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{1}{6 x ^{\frac{1}{2}}} - \frac{3 x ^{\frac{1}{2}}}{2}

(- 1 x y^{2} + 2 y) d x + (- 1 x^{2} y + 2 x) d y = 0

4 sec (θ)

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

\frac{d}{d x} ((5 x + 6)^{2})

f (x) = 4 x, at x = 9

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