Question
The graph of the function f, consisting of two line segments,is shown in the figure above. Let g be the function given by g(x)=2x+1,and let h be the fu.nction given by h(x)=f(g(x)).What is the value of \(h{}'(1)\)?
A -4
B -2
C 4
D 6
E nonexistent
▶️Answer/Explanation
Ans:A
Question
\(\frac{\mathrm{d} }{\mathrm{d} x}(\frac{1}{x^{3}}-\frac{1}{x+x^{2}})\) at x=-1 is
A -6
B -4
C 0
D 2
E 6
▶️Answer/Explanation
Ans:B
Question
\(y=\frac{1}{2}x^{\frac{4}{5}}-\frac{3}{x^{5}}\) then \(\frac{\mathrm{d} y}{\mathrm{d} x}\)=?
A \(\frac{2}{5x^{\frac{1}{5}}}+\frac{15}{x^{6}}\)
B \(\frac{2}{5x^{\frac{1}{5}}}+\frac{15}{x^{4}}\)
C \(\frac{2}{5x^{\frac{1}{5}}}-\frac{3}{5x^{4}}\)
D \(\frac{2x^{\frac{1}{5}}}{5}+\frac{15}{x^{6}}\)
E \(\frac{2x^{\frac{1}{5}}}{5}-\frac{3}{5x^{4}}\)
▶️Answer/Explanation
Ans:A
Question
Let
be the function defined by\(f(x)=bx^{2}-13bx+b^{2}+\frac{1}{x^{2}}\) where b is a nonzero constant. Which of the following is an expression for \(f{}'(x)\) ,the derivative of f
?
A \(2bx+3b-\frac{2}{x}\)
B \(2bx+3b-\frac{2}{x^{2}}\)
C \(2bx+3b+b^{2}-\frac{2}{x^{3}}\)
D \(x^{2}+3x+b\)
▶️Answer/Explanation
Ans:B
This question involves using the basic power rule for differentiation with respect to the independent variable x while treating the parameter b as a constant, as follows.
\(f(x)=\frac{\mathrm{d} }{\mathrm{d} x}(bx^{2}+3bx+b^{2}+x^{-2})\)
\(=2bx+3b+0+(-2)x^{-3}\)
\(=2bx+3b-\frac{2}{x^{3}}\)