How to Find the Derivative of b^x Using Logarithmic Differentiation and Chain Rule

Derivative of b^x

b^x ln(b)

The derivative of b^x with respect to x can be found using logarithmic differentiation or the chain rule.

Using logarithmic differentiation:

y = b^x
ln(y) = x * ln(b)
Differentiating both sides with respect to x gives:
1/y * dy/dx = ln(b)
Therefore,
dy/dx = y * ln(b) = b^x * ln(b)

Using the chain rule:

Let u = b^x
Then, du/dx = ln(b) * b^x * dx/dx = b^x * ln(b)
Therefore,
dy/dx = du/dx = b^x * ln(b)

Either method can be used to find the derivative of b^x with respect to x.

More Answers:

[next_post_link]

Share:

Recent Posts

Mathematics in Cancer Treatment

How Mathematics is Transforming Cancer Treatment Mathematics plays an increasingly vital role in the fight against cancer mesothelioma. From optimizing drug delivery systems to personalizing

Read More »