What is the derivative of 4t^{-3/8}+5ln(t)+ln(5) ?

The derivative of 4t^{-3/8}+5ln(t)+ln(5) is (10t^{11/8}-3t)/(2t^{19/8)}

What is the first derivative of 4t^{-3/8}+5ln(t)+ln(5) ?

The first derivative of 4t^{-3/8}+5ln(t)+ln(5) is (10t^{11/8}-3t)/(2t^{19/8)}

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derivative of

4 t^{- \frac{3}{8}} + 5 ln (t) + ln (5)

\frac{10 t ^{\frac{11}{8}} - 3 t}{2 t ^{\frac{19}{8}}}

Solution steps

\frac{d}{d t} (4 t^{- \frac{3}{8}} + 5 ln (t) + ln (5))

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (4 t^{- \frac{3}{8}}) + \frac{d}{d t} (5 ln (t)) + \frac{d}{d t} (ln (5))

\frac{d}{d t} (4 t^{- \frac{3}{8}}) = - \frac{3}{2 t ^{\frac{11}{8}}}

\frac{d}{d t} (5 ln (t)) = \frac{5}{t}

\frac{d}{d t} (ln (5)) = 0

= - \frac{3}{2 t ^{\frac{11}{8}}} + \frac{5}{t} + 0

Simplify

- \frac{3}{2 t ^{\frac{11}{8}}} + \frac{5}{t} + 0 : \frac{10 t ^{\frac{11}{8}} - 3 t}{2 t ^{\frac{19}{8}}}

= \frac{10 t ^{\frac{11}{8}} - 3 t}{2 t ^{\frac{19}{8}}}

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

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

- \frac{1}{2} x^{2}

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

\frac{\partial}{\partial z} (5 x sin (y - z))

What is the derivative of 4t^{-3/8}+5ln(t)+ln(5) ?
The derivative of 4t^{-3/8}+5ln(t)+ln(5) is (10t^{11/8}-3t)/(2t^{19/8)}
What is the first derivative of 4t^{-3/8}+5ln(t)+ln(5) ?
The first derivative of 4t^{-3/8}+5ln(t)+ln(5) is (10t^{11/8}-3t)/(2t^{19/8)}