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.
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