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

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

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

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

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

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

Solution steps

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

Simplify

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

\frac{d}{d x} (\frac{x ^{3} + 2}{cos ( x )})

\frac{d}{d x} (arcsin (x^{3} y))

\int e^{2 x} d x

\int_{1}^{e^{2}} \frac{3}{x} d x

\int \frac{1}{( 2 x + 5 ) ^{2}} d x

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