Question

Differentiate:
\[\LARGE (1-4x+7x^5)^{30}\]

Answer 1

by chain rule set \[u=1-4x+7x^5,\frac{du}{dx}=-4+35x^4\]
\[y=(1-4x+7x^5)^{30}=u^{30},\frac{dy}{du}=30u^{29}\]and use \[\frac{dy}{dx}=\frac{du}{dx}\frac{dy}{du}\] and substitute

Answer 2

\[30(1-4x+7x5)^{29}(1-4x+7x^{30})'\]

Answer 3

^^^ alternative method

Answer 4

Makes sense, thanks :)

Answer 5

@Luigi210 and @Luigi0210 Can you help me in health scicene

Answer 6

O.O

Answer 7

Another me? Great.

Answer 8

you have two accounts??? lol the one is 16 years old the other is 99

Answer 9

Can you?

Answer 10

um i guess

Answer 11

Okay go to heatlh scicens

Answer 12

theres a typo in the derivative
\[30(1-4x+7x^5)^{29}((1-4x+7x^5)^{30})'\]

Answer 13

It's a composite function and we want it's derivative:
Let's begin by recognizing the functions:
\[(1-4x+7x ^{5})^{30}\]
I said in an other question, that the derivative of a composite function is:
\[y=g(f(x))^{m}\]
\[y'=m.g(f(x))^{m-1}.f'(x)\]
meaning that the derivative of the function you showed is:
\[y'=30(1-4x+7x ^{5})^{29}(35x ^{4}-4)\]