Question

differentiate y=4e^x/sinx using quotient rule

Answer 1

quotient rule is just a specific type of the product rule. personally i like the product rule

Answer 2

to do this a product rule, you could simply pull the sin(x) above by giving it a -1 exponent

Answer 3

and do the simple uv'+vu'

Answer 4

\[\frac{4e^x}{sin(x)}=(4e^x)(sin(x))^{-1}\]

Answer 5

derivative would be uv'+vu'

\[(4e^x)(-1)(sin(x))^{-2}(cos(x))+sin(x)^{-1}(4e^x)\]

Answer 6

put the sin(x) back in the denominator and you'll get fractions that you'll need to creat a common denominator

Answer 7

\[\frac{-4e^x}{sin^2(x)}+\frac{4e^x}{sin(x)}\]

Answer 8

mutliply the last part by sin(x)/sin(x) to get the common denominator

Answer 9

\[\frac{-4e^x+4e^x(sin(x))}{sin^2(x)}\]

Answer 10

i forgot the cos(x) in the first part so just add that back in

Answer 11

\[\frac{-4e^xcosx+4e^xsinx}{sin^2(x)}\]