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

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

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

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

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derivative of

\frac{( 2 t + 1 ) ^{\frac{3}{2}}}{3}

(2 t + 1)^{\frac{1}{2}}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d t} (2 t + 1) = 2

= \frac{1}{3} \cdot \frac{3 ( 2 t + 1 ) ^{\frac{1}{2}}}{2} \cdot 2

Simplify

\frac{1}{3} \cdot \frac{3 ( 2 t + 1 ) ^{\frac{1}{2}}}{2} \cdot 2 : (2 t + 1)^{\frac{1}{2}}

= (2 t + 1)^{\frac{1}{2}}

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\frac{d}{d x} (6 (5 x^{2} + 2) x^{4} + 5)

x^{2} + 4, - x^{2} - 1, - 2, 3

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