document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199632>Question 199632</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Differentiate each function. Simplify all answers, with positive exponents, and with radical notation, where possible. Questions b and d must be in simplified factored form.<BR>\n" );
document.write( "a) y=(4x^5)-(3x^2)+(x/5)+2pi<BR>\n" );
document.write( "b) f(x)=(&#8730;x^4+2x^3-8)<BR>\n" );
document.write( "c) f(x)=(4(x^2)^3/2)-(8(x^3)^3/2)/2<BR>\n" );
document.write( "d) y=(2x-5)^4/(x+1)^3<BR>\n" );
document.write( "e) y=[x^2+(2x+1)^3]^5<BR>\n" );
document.write( "f) y=(&#8730;x-1)(x+1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150028 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=150028\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "For a) use <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x) = x^n \ \ \Rightarrow\ \ f'(x) = nx^{n-1}\"> and the fact that the derivative of the sum is the sum of the derivatives.\r<BR>\n" );
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document.write( "For b) do the same thing, but realize that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{x^4} = \left(\sqrt{x}\right)^4 = x^2\">\r<BR>\n" );
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document.write( "For c) remember that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (a^n)^m = a^{nm}\"> and then use the same process as for a)\r<BR>\n" );
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document.write( "For d) use the quotient rule:\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x) = \frac{g(x)}{h(x)}\"> where both <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g(x)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h(x)\"> are differentiable and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h(x) \neq 0\"> then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f'(x) = \frac{g'(x)h(x)-g(x)h'(x)}{\left(h(x)\right)^2\">\r<BR>\n" );
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document.write( "For e) use the chain rule:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}\">\r<BR>\n" );
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document.write( "But you will need to apply it twice working from the inside out.\r<BR>\n" );
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document.write( "For f) use the product rule:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x)=g(x)h(x) \ \ \Rightarrow\ \ f'(x) = g'(x)h(x)+g(x)h'(x)\">\r<BR>\n" );
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document.write( "If you want me to actually do these for you, write back and we'll talk.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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