derivative help plz

**helmszee** · October 1st 2007, 10:01 PM

cant work out how to use the math tag

need to find the derivative of (3+5t)^4t

i got

20(3+5t)^4t is that right if not need some help plz

**Soroban** · October 2nd 2007, 03:48 AM

Hello, helmszee!

We need logarithmic differentiation . . .

Differentiate: . $y \:=\:(3+5t)^{4t}$

Take logs: . $\ln y \;=\;\ln(3+5t)^{4t} \;=\;4t\cdot\ln(3+5t)$

Differentiate implicitly: . $\frac{1}{y}\cdot\frac{dy}{dt} \;=\;4t\cdot\frac{1}{3+5t}\cdot5 + 4\cdot \ln(3+5t) \;=\;\frac{20t}{3+5t} + 4\ln(3+5t)$

Multiply by $y\!:\;\;\frac{dy}{dt}\;=\;y\left[\frac{20t}{3+5t} + 4\ln(3+5t)\right]$

Replace $y\!:\;\;\frac{dy}{dt}\;=\;(3+5t)^{4t}\left[\frac{20t}{3+5t} + 4\ln(3+5t)\right]$

**Krizalid** · October 2nd 2007, 10:13 AM

Originally Posted by helmszee

need to find the derivative of (3+5t)^4t

You can also apply the famous trick $a=e^{\ln a},\,\forall a>0$

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