Differentiate y=(4x - 5)^5 by using the chain rule.
Notation: I use the ^ in the title question to indicated 'to the power of' and I use an asterisk * (or star) to indicate 'multiplied by' in the answer, to avoid confusion with the x term!
Step 1) let u = 4x - 5 therefore y = u5
Step 2) du/dx = 4 dy/du = 5u4
Step 3) (the chain rule!) dy/dx = dy/du * du/dx
so dy/dx = 5u4 * 4
dy/dx = 20u4
dy/dx = 20(4x - 5)4 as we substitute for the u term to complete our answer!
JE
Related Maths A Level answers
All answers ▸OCR C2 2015 Question 8: (a) Use logarithms to solve the equation 2^(n-3) = 18,000 , giving your answer correct to 3 significant figures. (b) Solve the simultaneous equations log2(x) + log2(y) = 8 & log2(x^2/y) = 7.
How does integration work?
What is the chain rule?
By writing tan x as sin x cos x , use the quotient rule to show that d dx ðtan xÞ ¼ sec2 x .