What is the derivative of 1/(2sqrt(t+4i))+2j ?

The derivative of 1/(2sqrt(t+4i))+2j is -1/(4(t+4i)^{3/2)}

What is the first derivative of 1/(2sqrt(t+4i))+2j ?

The first derivative of 1/(2sqrt(t+4i))+2j is -1/(4(t+4i)^{3/2)}

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derivative of

\frac{1}{2 t + 4 i} + 2 j

- \frac{1}{4 ( t + 4 i ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d t} (\frac{1}{2 t + 4 i} + 2 j)

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (\frac{1}{2 t + 4 i}) + \frac{d}{d t} (2 j)

\frac{d}{d t} (\frac{1}{2 t + 4 i}) = - \frac{1}{4 ( t + 4 i ) ^{\frac{3}{2}}}

\frac{d}{d t} (2 j) = 0

= - \frac{1}{4 ( t + 4 i ) ^{\frac{3}{2}}} + 0

Simplify

= - \frac{1}{4 ( t + 4 i ) ^{\frac{3}{2}}}

\int_{0}^{1} arctan (4 x) d x

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

\int sin (\frac{nπ x}{5}) d x

y^{^{'}} = \frac{1}{x} y

x \to 0 - lim (e^{\frac{1}{x}})

What is the derivative of 1/(2sqrt(t+4i))+2j ?
The derivative of 1/(2sqrt(t+4i))+2j is -1/(4(t+4i)^{3/2)}
What is the first derivative of 1/(2sqrt(t+4i))+2j ?
The first derivative of 1/(2sqrt(t+4i))+2j is -1/(4(t+4i)^{3/2)}