What is the derivative of x32log2√x+1? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions without Base e 1 Answer maganbhai P. Mar 13, 2018 √x2ln2[xx+1+3⋅ln√x+1] Explanation: Note:(1)logab=logeblogea (2)ddx(u⋅v)=u⋅dvdx+v⋅dudx y=x32log2√x+1=x32[loge√x+1loge2] y=1loge2⋅x32⋅loge√x+1 y=1ln2⋅x32⋅ln√x+1 dydx=1ln2[x32ddx(ln√x+1)+ln√x+1ddx(x32)] =1ln2[x32⋅1√x+1⋅12√x+1+ln√x+1⋅32⋅x12] =1ln2[x⋅√x2(x+1)+32⋅√x⋅ln√x+1] =√x2ln2[xx+1+3⋅ln√x+1] Answer link Related questions What is the derivative of f(x)=logb(g(x)) ? What is the derivative of f(x)=log(x2+x) ? What is the derivative of f(x)=log4(ex+3) ? What is the derivative of f(x)=x⋅log5(x) ? What is the derivative of f(x)=e4x⋅log(1−x) ? What is the derivative of f(x)=log(x)x ? What is the derivative of f(x)=log2(cos(x)) ? What is the derivative of f(x)=log11(tan(x)) ? What is the derivative of f(x)=√1+log3(x) ? What is the derivative of f(x)=(log6(x))2 ? See all questions in Differentiating Logarithmic Functions without Base e Impact of this question 1740 views around the world You can reuse this answer Creative Commons License