C4 – Exam Tip #1

Differentiating y=a^x

As part of the C4 content, you must know how to differentiate y=a^x where a is a constant.

The trick to finding \frac{dy}{dx} when y=a^x is first taking the natural logarithm of both sides of this equation:


Then use the laws of logarithms to bring the x outside:


We can then differentiate both sides of this equation (this means differentiating the left hand side implicitly):


Note that ln(a) is a constant and so x\ln(a)

Finally, multiply both sides of the equation by y


…and remember that y=a^x