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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d t} (0.3 cos (30 t))

csc^{3} (x)

2 x^{2} - x + 1

y = 2 x^{2} + 3 x \cdot tan (x)

f (x) = 10 - 5 x

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