Question

differentiate: y= (3x^2 - 4x + 5)^4

Answer 1

do u know the rules of differentiation

Answer 2

do you?

Answer 3

u must write w.r.t. to what

Answer 4

Let
\[\Large t=3x^2-4x+5\]
\[\Large \implies y=t^4\]
now differentiate y with respect to t and differentiate t with respect to x , then use chain rule
\[\Large \frac{dy}{dx}=\frac{dy}{dt}*\frac{dt}{dx}\]

\[\Large \frac{dy}{dt}=4t^3\]
\[\Large \frac{dt}{dx}=6x-4\]
just use chain rule now
\[\Large \frac{dy}{dx}=\frac{dy}{dt}*\frac{dt}{dx}\]

Answer 5

y=f(g(x))
dy/dx = f'(x) x g'(x)

so y=(3x^2-4x+5)^4
dy/dx= 4(3x^2-4x+5) (6x-4)

Answer 6

hmm.. what is the final answer?

Answer 7

dy/dx= 4(3x^2-4x+5) (6x-4)

in factorised form

Answer 8

4(3x^2-4x+5)^3 (6x-4)
opps sorry missed a ^3

Answer 9

then after that, i will simplify that?

Answer 10

usually you don't need to~ they usually prefer answer in factorised form~ so that will be the final answer :)

Answer 11

ahh! thank you so much .. now, i know!