Derivative

[Ryan Rigdon]

Find Dxy. y=tan^(4)x

my work

y = tan^(4) x = (tan^(2) x)(tan^(2) x)

y ' = tan^(2) x * sec^(4) x + tan^(2) x * sec^(4) x


where do i go from here?

 

[Deleted member 4993]

Find Dxy. y=tan^(4)x

my work

y = tan^(4) x = (tan^(2) x)(tan^(2) x)

y ' = tan^(2) x * sec^(4) x + tan^(2) x * sec^(4) x


where do i go from here?

I am assuming you want find dy/dx when y = tan^(4)x

You'll need to use "power rule" and "chain rule" as follows:

\(\displaystyle \frac{d}{dx} [tan^4(x)] \ \ = \ \ 4 * [tan^3(x)] * sec^2(x)\)

 

[Ryan Rigdon]

[quote="Ryan Rigdon":17giae4i]Find Dxy. y=tan^(4)x

my work

y = tan^(4) x = (tan^(2) x)(tan^(2) x)

y ' = tan^(2) x * sec^(4) x + tan^(2) x * sec^(4) x


where do i go from here?

I am assuming you want find dy/dx when y = tan^(4)x

You'll need to use "power rule" and "chain rule" as follows:

\(\displaystyle \frac{d}{dx} [tan^4(x)] \ \ = \ \ 4 * [tan^3(x)] * sec^2(x)\)[/quote:17giae4i]



I know that Dx tan x = sec^(2) x

how can Dx tan^(4) x = sec^(2) x?

 

[Ryan Rigdon]

i figured it out

y = tan^(4) x

Power & Chain Rule

y ' = [tanx]^4

= 4tan^(3) x * (derivative of the inside which is sec^(2) x)

hence y ' = 4tan^(3) x * sec^(2) x