How do you find a derivative of a function?
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Answer:
d/dx (6x^2 + 2x - 1)^7 = 7(6x^2 + 2x - 1)^6 * d/dx (6x^2 + 2x -1) = 7(6x^2 + 2x - 1)^6 * (12x + 2) = 14(6x + 1) * (6x^2 + 2x -1)^6.
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Other answers
Let u=6x^2+2x-1 & y=(6x^2+2x-1)^7. So y=(6x^2+2x-1)^7=u^7. Diff. both sides w.r.t u we get dy/du=7*(u^6) ------(i) Also diff. both sides of u=6x^2+2x-1 w.r.t. x we get du/dx=12*x+2 ------(ii) Now, by chain rule dy/dx=(dy/du)*(du/dx)=7(u^6)(12x+2)=14… [ANSWER]
RitamGanguly
Let u=6x^2+2x-1 & y=(6x^2+2x-1)^7. So y=(6x^2+2x-1)^7=u^7. Diff. both sides w.r.t u we get dy/du=7*(u^6) ------(i) Also diff. both sides of u=6x^2+2x-1 w.r.t. x we get du/dx=12*x+2 ------(ii) Now, by chain rule dy/dx=(dy/du)*(du/dx)=7(u^6)(12x+2)=14... [ANSWER]
RitamGanguly
The easy way is to go to http://wolframalpha.com and enter "derivative of (6x^2 + 2x - 1)^7" That won't teach you how to do it yourself, however, if that's what you're looking for.
sethgrimes
d/dx (6x^2 + 2x - 1)^7 = 7(6x^2 + 2x - 1)^6 * d/dx (6x^2 + 2x -1) = 7(6x^2 + 2x - 1)^6 * (12x + 2) = 14(6x + 1) * (6x^2 + 2x -1)^6.
Madhukar
This is simple chain rule differentiation: Basically, its the derivative of the bracket itself x the derivative of whats in the bracket so: dy dx = 7(6x^2 + 2x + 1)^6.(12x + 2) which simplifies too --> (84x + 14)(6x^2 + 2x + 1)^6 :]
TheKnight
(6x^2 + 2x - 1)^7 derivative = { 7(6x^2 + 2x - 1)^6} . (12x+2-0)
iyiogrenci
f ` ( x ) = 7 ( 6 x ² + 2 x - 1 )^6 ( 12 x + 2 )
Como
This is simple chain rule differentiation: Basically, its the derivative of the bracket itself x the derivative of whats in the bracket so: dy dx = 7(6x^2 + 2x + 1)^6.(12x + 2) which simplifies too --> (84x + 14)(6x^2 + 2x + 1)^6 :]
TheKnight
f ` ( x ) = 7 ( 6 x ² + 2 x - 1 )^6 ( 12 x + 2 )
Como
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