Question

find the derivative of y with respect to x, t or theta.
(a) e^7 - 10x
Answer: -10e^7-10x
(b) 8xe^x - 8e^x
answer: 8xe^x
(c) y= (x^2 -2x+4)e^x
answer: (x^2+2)e^x
(d) y= sin e^theta^4
answer: (-4theta^3 e^-theta^4) cos e^-theta^4

please show the steps. thank you

Answer 1

The first one is \[\Large e^{7-10x}\] right?

Answer 2

yes

Answer 3

The derivative of that isn't -10e^7-10x, so there has to be a typo somewhere

Answer 4

im not sure i think we have to use the u substitution method to find the answer.

Answer 5

oh wait, is the answer is \[\Large -10e^{7-10x}\] and not \[\Large -10e^{7}-10x\]

Answer 6

yea its the first one

Answer 7

this is why parenthesis are useful

if 7-10x is in the exponent, then say e^(7-10x)

Answer 8

ok that makes more sense now

Answer 9

sorry about that

Answer 10

let u = 7 - 10x, which means du/dx = -10

this means

\[\Large e^{7-10x}\]

turns into

\[\Large e^{u}\]

then derive to get

\[\Large e^{u}*\frac{du}{dx}\]

\[\Large e^{u}(-10)\]

\[\Large -10e^{u}\]

\[\Large -10e^{7-10x}\]

Answer 11

I'm using the chain rule, which is

If h(x) = f(g(x)), then

h ' (x) = f ' (g(x)) * g ' (x)

Answer 12

ok i just need help with the other 3 as well

Answer 13

whats the derivative of 8xe^x

Answer 14

im not sure

Answer 15

use the product rule

Answer 16

tell me what you get

Answer 17

is it 8xe^x

Answer 18

no, but that's part of it though

Answer 19

Product Rule:

if h(x) = f(x)*g(x), then

h ' (x) = f ' (x) * g(x) + f(x) * g ' (x)