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How do you find the derivative of #3^x#?

Answer 1

Charles Anctil

#(dy)/(dx)=3^xln3#

using logarithmic differentiation

#y=3^x#

take natural logs to both sides

#lny=ln3^x=xln3#

differentiate #wrt" " x#

#1/y(dy)/(dx)=ln3#

#(dy)/(dx)=yln3#

substitute back

#(dy)/(dx)=3^xln3#

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Answer 2

Evelyn Agard

To find the derivative of (3^x), you use logarithmic differentiation. The derivative is (3^x) times the natural logarithm of the base, which is (3), multiplied by (dx). So, the derivative of (3^x) with respect to (x) is (3^x \ln(3)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.