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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x - 1) = 1

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

Simplify

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

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

\int \frac{( ln ( x ) ) ^{2}}{x ^{3}} d x

y^{^{'}} = - 2 x e^{2 x}, y (0) = 1

\frac{1}{s ^{1} ( s + 1 ) ^{3}}

f (x) = x^{2} - 4, - 3, 1

\int x x d x

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