# Math Help - implicit differentiation

1. ## implicit differentiation

$

3{^x}+log{_2}(xy)=10

$

2. Originally Posted by simsima_1
$

3{^x}+log{_2}(xy)=10

$
The derivative of the right hand side with respect to x is zero.

The derivative of the left hand side with respect to x requires differentiating $3^x$ and $\log{_2} (xy)$ with respect to x.

Note that:

1. The derivative of $y = a^x$ with resepct to x is $(\ln a) \, a^x$

2. The derivative of $y = \log_{a} x$ with resepct to x is $\left( \frac{1}{\ln a} \right) \, \frac{1}{x}$

for appropriate values of a.

Note also that you get the derivative of xy by using the product rule .....