<p>What is the derivative of cos3X?
the 3 is a power,in another way-cube cosX</p>
<p>My answer is 3 times cos2X(2 is a power),is that correct?</p>
<p>y = cos(x)^3</p>
<p>y` = (3cos(x)^2) * -sin(x)</p>
<p>^ That’s right. One must apply the chain rule to the cosine function.</p>
<p>thank you.</p>
<p>Ok,I have got another problem:ln(cos^5X),so what is the dy/dx
Thank you very much:)</p>
<p>(1/(cos(x)^5)) * 5cos(x)^4 * -sin(x)</p>
<p>One must do the chain rule twice.</p>
<p>Thanks.:))</p>
<p>Sry,maybe i didn’t ask clearly,the 5 is a power,which means ln[(cosx)^5],and the correct answer is -5tanx,but how to solve it?Thank you.</p>
<p>If you simplify my answer in post #7, it comes out to -5tan(x).</p>
<p>I get it,thank you.So if i don’t simplify the original answer,am i counted as correct?</p>
<p>I don’t know the simplification rules for the AP test. In my class, however, the unsimplified form would be half credit.</p>
<p>Thank you:)))</p>
<p>Anyone one can help with a question?
what’s the y’ of siny=e^x
Thank you!</p>
<p>(cos y)(y`) = e^x
y` = (e^x)/(cosy)</p>
<p>Thank you!</p>
<p>Thank you for helping me this one
-whats the y’ of y=x^x
my answer is still x^x,what’s wrong with my answer?</p>
<p>You get that if you try to use the power rule. Problem is, the power rule ONLY works for constant powers.</p>
<p>f’x = x^x*log(x)+x^x</p>
<p>y = x^x</p>
<p>ln y = x ln x</p>
<p>(1/y)(y`) = ln x + 1</p>
<p>y<code>= (ln x + 1) / (1/y)
y</code> = ylnx + y</p>
<p>Since y = x^x…</p>
<p>y1 = (x^x)(ln x) + (x^x)</p>