How do you differentiate $y = 5^{\frac{3 x}{2}}$ $y=5^((3x)/2)$ ?

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Answer 1 · 2016-09-11T12:43:30

$\frac{3 ln (5)}{2} \cdot 5^{\frac{3 x}{2}}$ $(3 ln(5)) / (2) cdot 5^((3 x) / (2))$

We have: $y = 5^{\frac{3 x}{2}}$ $y = 5^((3 x) / (2))$

This function can be differentiated using the "chain rule".

Let $u = (3 x) / (2) => u' = (3) / (2)$ and $v = 5^(u) => v' = 5^(u) (ln(5))$ :

$=> y' = (3) / (2) cdot 5^(u) (ln(5))$

$=> y' = (3 ln(5)) / (2) cdot 5^(u)$

We can now replace $u$ with $(3 x) / (2)$ :

$=> y' = (3 ln(5)) / (2) cdot 5^((3 x) / (2))$

How do you differentiate y=5^((3x)/2)y=53x2y=5^((3x)/2)?