What is the derivative of f(x)=(5x^{3/2}-15^{1/2})/2 ?

The derivative of f(x)=(5x^{3/2}-15^{1/2})/2 is (15x^{1/2})/4

What is the first derivative of f(x)=(5x^{3/2}-15^{1/2})/2 ?

The first derivative of f(x)=(5x^{3/2}-15^{1/2})/2 is (15x^{1/2})/4

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derivative of

f (x) = \frac{5 x ^{\frac{3}{2}} - 1 5 ^{\frac{1}{2}}}{2}

\frac{15 x ^{\frac{1}{2}}}{4}

Solution steps

\frac{d}{d x} (\frac{5 x ^{\frac{3}{2}} - 1 5 ^{\frac{1}{2}}}{2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{d}{d x} (5 x^{\frac{3}{2}} - 1 5^{\frac{1}{2}})

Apply the Sum/Difference Rule:

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

= \frac{1}{2} (\frac{d}{d x} (5 x^{\frac{3}{2}}) - \frac{d}{d x} (1 5^{\frac{1}{2}}))

\frac{d}{d x} (5 x^{\frac{3}{2}}) = \frac{15 x ^{\frac{1}{2}}}{2}

\frac{d}{d x} (1 5^{\frac{1}{2}}) = 0

= \frac{1}{2} (\frac{15 x ^{\frac{1}{2}}}{2} - 0)

Simplify

\frac{1}{2} (\frac{15 x ^{\frac{1}{2}}}{2} - 0) : \frac{15 x ^{\frac{1}{2}}}{4}

= \frac{15 x ^{\frac{1}{2}}}{4}

What is the derivative of f(x)=(5x^{3/2}-15^{1/2})/2 ?
The derivative of f(x)=(5x^{3/2}-15^{1/2})/2 is (15x^{1/2})/4
What is the first derivative of f(x)=(5x^{3/2}-15^{1/2})/2 ?
The first derivative of f(x)=(5x^{3/2}-15^{1/2})/2 is (15x^{1/2})/4