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How to differentiate this?
y = x^7(3x^4 + 12x - 1)^2
Just needed the rules, thank you!
3 Answers
- RayLv 77 years ago
Product rule: (f*g)'= f 'g + f g'
y'= 7x^6*(3x^4+12x-1)^2 + x^7* 2(3x^4+12x-1)* (4x^3+12)
(3x^4+12x-1)(21x^10 +84x^7 -7x^6 +8x^3 +24)
- RogueLv 77 years ago
y = x^7(3x^4 + 12x − 1)^2
=> dy/dx = d/dx( x^7(3x^4 + 12x − 1)^2 )
using the product rule d/dx(uv) = u * dv/dx + v * du/dx
=> dy/dx = x^7 * d/dx((3x^4 + 12x − 1)^2) + (3x^4 + 12x − 1)^2 * d/dx(x^7)
using the chain rule d/dx(u^n) = nu^(n − 1) * d/dx(u)
=> dy/dx = x^7 * 2(3x^4 + 12x − 1) * d/dx((3x^4 + 12x − 1)) + (3x^4 + 12x − 1)^2 * d/dx(x^7)
going term by term
=> dy/dx = 2x^7(3x^4 + 12x −1)(d/dx(3x^4) + d/dx(12x) − d/dx(1)) + (3x^4 + 12x − 1)^2 * d/dx(x^7)
using the power rule d/dx(x^n) = nx^(n−1(
=> dy/dx = 2x^7(3x^4 + 12x −1)(12x^3 + 12) + 7x^6(3x^4 + 12x − 1)^2
simplfiy
=> dy/dx = x^6(3x^4 + 12x −1)[2x(12x^3 + 12) + 7(3x^4 + 12x − 1)]
=> dy/dx = x^6(3x^4 + 12x −1)[24x^4 + 24x + 21x^4 + 84x − 7]
=> dy/dx = x^6(3x^4 + 12x −1)(45x^4 + 108x − 7)
