How do you differentiate f(x)=sec(1√3x2−4) using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer maganbhai P. Jun 26, 2018 dydx=−3x(3x2−4)32sec(1√3x2−4)tan(1√3x2−4) Explanation: Let , y=secu , u=1vandv=√3x2−4 ⇒dydu=secutanu, dudv=−1v2and dvdx=12√3x2−4ddx(3x2−4)=6x2√3x2−4=3x√3x2−4 Using chain rule: dydx=dydu⋅dudv.dvdx dydx=secutanu(−1v2)3x√3x2−4,where,u=1v dydx=sec(1v)tan(1v)(−1v2)3x√3x2−4 Putting , v=√3x2−4 dydx=−sec(1√3x2−4)tan(1√3x2−4)13x2−4⋅3x√3x2−4 dydx=−3x(3x2−4)32sec(1√3x2−4)tan(1√3x2−4) Answer link Related questions What is the Chain Rule for derivatives? How do you find the derivative of y=6cos(x2) ? How do you find the derivative of y=6cos(x3+3) ? How do you find the derivative of y=ex2 ? How do you find the derivative of y=ln(sin(x)) ? How do you find the derivative of y=ln(ex+3) ? How do you find the derivative of y=tan(5x) ? How do you find the derivative of y=(4x−x2)10 ? How do you find the derivative of y=(x2+3x+5)14 ? How do you find the derivative of y=(1+x1−x)3 ? See all questions in Chain Rule Impact of this question 1561 views around the world You can reuse this answer Creative Commons License