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What is the derivative of #5^x#?

Answer 1

Christopher Agresta

#5^xln5#

Given: #d/dx(5^x)#.

Apply the general formula that #d/dx(a^x)=a^xlna \ "for" \ ainRR#.

#:.d/dx(5^x)=5^xln5#

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Answer 2

Samantha Adkison

#5^xln5#

#"let "y=5^x#

#"differentiate "color(blue)"implicitly with respect to x"#

#"take ln (natural log) of both sides"#

#lny=ln5^x=xln5#

#rArr1/ydy/dx=ln5#

#rArrdy/dx=yln5=5^xln5#

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Answer 3

Paisley Johnson

The derivative of (5^x) is (5^x \ln(5)).

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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.