What is the derivative of 2^(2x)?

1 Answer
Jun 5, 2016

=2^{2x+1}ln (2)

Explanation:

frac{d}{dx}(2^{2x})
Applying exponent rule,a^b=e^{bln (a)}

2^{2x}=e^{2xln (2)}
=frac{d}{dx}(e^{2x\ln (2)})

Applying chain rule,
frac{df(u)}{dx}=frac{df}{du}cdot frac{du}{dx}

Let, 2xln (2)=u
=frac{d}{du}(e^u)frac{d}{dx}(2xln (2))

We know,
frac{d}{du}(e^u)=e^u
and,
frac{d}{dx}(2xln (2))=2ln (2)

Also,
=e^u2ln (2)

Substituting back,u=2xln (2)

Simplifying it,
=2^{2x+1}ln (2)