Find the derivative of:
When t = 2, my calculator says it should be about 36.
Could you also please show the steps?
Thanks Guys!
Hello,
$\displaystyle H(t)=9000 \cdot \frac{\ln \left(\frac t4+1\right)}{t^2+25}$
Use the quotient rule : $\displaystyle \left(\frac uv\right)'=\frac{u'v-uv'}{v^2}$
Here :
$\displaystyle u(t)=\ln \left(\frac t4+1\right) \implies u'(t)=\frac{\frac 14}{\frac t4+1}=\frac{1}{4 \left(\frac t4+1\right)}$
$\displaystyle v(t)=t^2+25 \implies v'(t)=2t$
$\displaystyle \begin{aligned} H'(t) &=9000 \cdot \left(\frac{\ln \left(\frac t4+1\right)}{t^2+25}\right)' \\
&=9000 \cdot \frac{\frac{1}{4 \left(\frac t4+1\right)} \cdot (t^2+25)-\ln \left(\frac t4+1\right)\cdot 2t}{(t^2+25)^2} \end{aligned}$
You should be able to continue..