What is the derivative of ln(x^2)+5^(2x)?

1 Answer
Oct 14, 2016

dy/dx = 2/x + (2ln(5))5^(2x)

Explanation:

Term-by-term

Term 1:

Before you differentiate use the identity ln(x^a) = aln(x)

2(d[ln(x)])/dx = 2/x

Term 2:

Use logarithmic differentiation:

y = 5^(2x)

ln(y) = ln(5)2x

1/ydy/dx = 2ln(5)

dy/dx = (2ln(5))5^(2x)

Put the two terms back together:

dy/dx = 2/x + (2ln(5))5^(2x)