Question

Calculate the derivative of the function
(Using Chain Rule)

f(x) = (6.4x − 7)^-2 + (4.3x − 6)^-2

Answer 1

y=x^n
then y'=nx^n-1
try it here
f(x) = (6.4x − 7)^-2 + (4.3x − 6)^-2

Answer 2

the chain rule yields
\[f \prime \left( x \right)=-2\left( 6.4x-7 \right)^{-3}\left( 6.4 \right)+\left( -2 \right)\left( 4.3x-6 \right)^{-3}\left( 4.3 \right)\]

Answer 3

you would first differentiate the stuff inside the brackets and then the outside. So you treat whatever is inside like it was a function on its own (I assume you know what a function is)

So lets call the first expression

A = \[(6.4x - 7)^{-2} \]
B = \[(4.3x -6)^{-2}\]

\[\frac{ df(x) }{ dx }=\frac{ df(x) }{ dA }\frac{ dA }{ dx }+\frac{ df(x) }{ dB }\frac{ dB }{ dx }\]

This would be the chain rule to follow. So you use the standard rule \[f \prime = nx ^{n-1}\] to calculate each derivative, then multiply them together and add them to get your final answer.

Sorry if it is too long to follow but hope you get to the answer!

Answer 4

ok so i understand the format, but when f'(x)= -2(6.4x-7)^-2 (6.4)

im having a bit of hard time multiplying it out

Answer 5

@sirm3d what do i do with the (6.4) on the first part of the equation? im having a hard time multiplying it out

Answer 6

multiply it with -2 to get \[-12.8\left( 6.4x-7 \right)^{-3}\]

Answer 7

ok so i got -8.6(4.3x-6)^-3

from there what do i do

Answer 8

the problem is solved.

Answer 9

@sirm3d thanks a lot for the help

Answer 10

quick question, where did u get (-3) for the square

Answer 11

the differentiation rule for \[x^{n}\] requires that you subtract 1 from the exponent

Answer 12

oh yes thats right so it would of been -2-1 = -3

Answer 13

that's right