Find the derivative of f(x) = (sin^2(x) tan^4(x))/e^(x^2)
I made the fraction into multiplication and then applied the product rule. I got stuck at the e side!
I made the fraction into multiplication and then applied the product rule. I got stuck at the e side!
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Quotient rule:
bottom(derivative of top) - top(derivative of bottom) all over the bottom squared
{[e^(x^2)] x [2sinxcosx + 4tan^3xsec^2x] - [(sin^2xtan^4x) x 2xe^(x^2)]} / (e^(x^2))^2
notice that an e^(x^2) is in every spot so cancel one out. so then you get:
{2sinxcosx + 4tan^3xsec^2x - 2xsin^2xtan^4x} / e^(x^2)
then you can factor stuff out...the 2 can go outside, you can factor out a sin but that would be unecesary.
bottom(derivative of top) - top(derivative of bottom) all over the bottom squared
{[e^(x^2)] x [2sinxcosx + 4tan^3xsec^2x] - [(sin^2xtan^4x) x 2xe^(x^2)]} / (e^(x^2))^2
notice that an e^(x^2) is in every spot so cancel one out. so then you get:
{2sinxcosx + 4tan^3xsec^2x - 2xsin^2xtan^4x} / e^(x^2)
then you can factor stuff out...the 2 can go outside, you can factor out a sin but that would be unecesary.