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the horizontal axis is the bottom (____), the title is usually hiden in the task name
Given exponential function:
Let us obtain three points including the y-intercept so that we can plot the function y = f(x)
When x =0:
when x =1:
when x =2:
We have the points : (0, 1), (1, 1/5), and (2, 1/25)
Using these points, let us provide a sketch of the plot of y =f(x). We have the plot as shown below:
Use the power, product, and chain rules:
• product rule
• power rule for the first term, and power/chain rules for the second term:
• power rule
Now simplify.
You could also use logarithmic differentiation, which involves taking logarithms of both sides and differentiating with the chain rule.
On the right side, the logarithm of a product can be expanded as a sum of logarithms. Then use other properties of logarithms to simplify
Differentiate both sides and you end up with the same derivative: