Find the derivative of sqrt(3x-5) using the definition of the derivative. Help?

1 Answer
Jim G.
May 21, 2018

3/(2sqrt(3x-5))

Explanation:

"using differentiation from first principles"

•color(white)(x)f'(x)=lim_(hto0)(f(x+h)-f(x))/h

rArrf'(x)=lim_(hto0)(sqrt(3(x+h)-5)-sqrt(3x-5))/h

"multiply numerator/denominator by the conjugate of "
"the numerator"

=lim_(hto0)((sqrt(3(x+h)-5)-sqrt(3x-5))(sqrt(3(x+h)-5)+sqrt(3x-5)))/(h(sqrt(3(x+h)-5)+sqrt(3x-5))

=lim_(hto0)(3(x+h)-5-(3x-5))/(h(sqrt(3(x+h)-5)+sqrt(3x-5))

=lim_(hto0)(3x+3h-5-3x+5)/(h(sqrt(3(x+h)-5)+sqrt(3x-5))

=lim_(hto0)(3cancel(h))/(cancel(h)sqrt(3(x+h)-5)+sqrt(3x-5))

=3/(sqrt(3x-5)+sqrt(3x-5))=3/(2sqrt(3x-5))

Related questions
Impact of this question
6269 views around the world
You can reuse this answer
Creative Commons License