document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=200743>Question 200743</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can someone help please<BR>\n" );
document.write( "My teacher is asking which of these statements is/are true select all that apply<BR>\n" );
document.write( "1.  if F(x)=f(x)*g(x), then F'(x)=f'(x)*g'(x)<BR>\n" );
document.write( "2.  if c is a constant, then d/dx(c*f(x))=c*d/dx(f(x))<BR>\n" );
document.write( "3.  if c is a constant, then d(c)/dx=0<BR>\n" );
document.write( "4. if F(x)-f(x)+g(x), then F'(x)=f'(x)+g'(x)<BR>\n" );
document.write( "5.  if F(x)=f(x)*g(x), then F'(x)=f(x)*g'(x)+g(x)*f'(x)<BR>\n" );
document.write( "6.  none of these<BR>\n" );
document.write( "7. if k is a real number, then d(x^k)/dx=kx^k-1\r<BR>\n" );
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document.write( "thanks a bunch<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150999 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=150999\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. <font color=red>False</font>. This is NEVER true and it is a misconception to many incoming calc students. Why? Well you first learn that if F(x)=f(x)+g(x), then F'(x)=f'(x)+g'(x). So many people wonder: \"why not apply it to f(x)*g(x)?\"\r<BR>\n" );
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document.write( "2. <font color=red>True</font>. The derivative is a linear operator. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2F%28dx%29%29%28m%2Af%28x%29%2Bn%2Ag%28x%29%29=m%2A%28d%2F%28dx%29%29%28f%28x%29%29%2Bn%2A%28d%2F%28dx%29%29%28g%28x%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > where \"m\" and \"n\" are constants.\r<BR>\n" );
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document.write( "3. <font color=red>True</font>. Recall that a constant function graphs a horizontal line. Also, the slope of ANY horizontal line is zero.\r<BR>\n" );
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document.write( "4. I'm assuming you meant to write F(x)=f(x)+g(x). If so, then this is <font color=red>true</font>. Once again, the derivative is a linear operator.\r<BR>\n" );
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document.write( "5. This is <font color=red>true</font> (as this is the definition of the product rule).\r<BR>\n" );
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document.write( "6. <font color=red>False</font> (since at least one is true, this is automatically false)\r<BR>\n" );
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document.write( "7. <font color=red>True</font>. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%28x%5Ek%29%2F%28dx%29=k%2Ax%5E%28k-1%29 ALIGN=MIDDLE  ALT=\"d%28x%5Ek%29%2F%28dx%29=k%2Ax%5E%28k-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Example: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%28x%5E3%29%2F%28dx%29=3x%5E%283-1%29=3x%5E2 ALIGN=MIDDLE  ALT=\"d%28x%5E3%29%2F%28dx%29=3x%5E%283-1%29=3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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