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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (3) = 0

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

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

Simplify

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

\int \frac{sin ( \frac{1}{x ^{7}} )}{x ^{8}} d x

\int \frac{sin ^{7} ( 7 x )}{cos ^{4} ( 7 x )} d x

ln (12 x)

\frac{d}{d x} (sin (\frac{π x}{5}))

y = \frac{6 x}{3 - cot ( x )}

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