Question

Determine and simplify dy/dx:

Answer 1

cancel the \(d\)'s top and bottom and get
\[\frac{y}{x}\]

Answer 2

can't read it sorry

Answer 3

\[y=tanx/xcosx\]

Answer 4

\[y=x ^{7}e ^{x ^{7}}+8^{x-1}\times4^{-x ^{2}-secx ^{3}}\]

Answer 5

first one requires the quotient rule , also the product rule
\[\left(\frac{f}{g}\right)'=\frac{gf'-fg'}{g^2}\]with
\[f(x)=\tan(x), f'(x)=\sec^2(x), g(x)=x\cos(x), g'(x)=\cos(x)-x\sin(x)\]

Answer 6

second one is going to be a real pita
the first part is not too bad,
\[(fg)'=f'g+g'f\] with
\[f(x)=x^7, f'(x)=7x^6, g(x)=e^{x^7}, g'(x)=7x^6e^{x^7}\]

Answer 7

second part is going to be just a total mess
\[\frac{d}{dx}8^{x-1}=\ln(8)8^{x-1}\]

Answer 8

i think @FibonacciChick666 will finish finding the derivative of
\[\large 4^{-x^2-\sec(x^3)}\]

Answer 9

who makes up these functions?

Answer 10

... you have to be kidding me... that's just evil

Answer 11

alright, so first, let's clean up the given

Answer 12

that isn't multiplication of the x^2 is it...

Answer 13

oh yuck

Answer 14

and actually @satellite73 it's this: \[y=x ^{7}e ^{x ^{7}}+8^{x-1}.4^{-x ^{2}-Secx ^{3}}\]according to the word document

Answer 15

yes, please go with the word document question

Answer 16

so just the \(.4^{-x^2-secx^3}\) for me. first we need to substitute in for the exponent so let's set \(g=-x^2-secx^3\) so all you have to do @Jas1997 is find the derivative of \(.4^g\) then what the derivative of g is for the second part of the product rule.

Answer 17

step by step solution
http://www.mathskey.com/question2answer/17510/derivative

Answer 18

Thankyou @bradely @FibonacciChick666 @satellite73