TEST 9
1.
\(f(x)=3x-1\)
\(g(x)=x^2+2\)
\(\Rightarrow(f\circ g)'(x)=?\)
A) \(6x\)B) \(6x^2+12\)C) \(6x-3\)D) \(3x^2-6\)E) \(3x^2+6\)
2.
\(f(x)=2x^2+5x\)
\(g(x)=x^2-3\)
\(\Rightarrow(f\circ g)'(x)=?\)
A) \(8x^2-1\)B) \(4x^2+4\)C) \(x^2+6\)D) \(8x^3-14x\)E) \(8x^3-x\)
3.
\(f(x)=x^3-3\)
\(g(x)=3x^2+1\)
\(\Rightarrow(f\circ g)'(1)=?\)
A) \(252\)B) \(288\)C) \(300\)D) \(312\)E) \(324\)
4.
\(f(x)=\sin^2x\)
\(g(x)=x^2+1\)
\(\Rightarrow(g\circ f)'\left(\samefrac{\pi}{2}\right)=?\)
A) \(-2\)B) \(-1\)C) \(0\)D) \(1\)E) \(2\)
5.
\(f(x)=x^2+1\)
\(g(x)=\sin x\)
\(\Rightarrow(f\circ g)'(x)=?\)
A) \(\sin(2x)\)B) \(\sin x+1\)C) \(\sin x\cdot\cos x\)D) \(\cos x-\sin x\)E) \(0\)
6.
\(f(x)=x^2\)
\(g(x)=\samefrac1{x^2}\)
\(\Rightarrow(g\circ f)'(1)=?\)
A) \(-4\)B) \(-\samefrac{4}{5}\)C) \(1\)D) \(\samefrac{1}{5}\)E) \(4\)
7.
\(\left.\begin{gathered}g'(-1)=5\\g(-1)=3\\f'(3)=4\end{gathered}\right\}\Rightarrow(f\circ g)'(-1)=?\)
A) \(10\)B) \(15\)C) \(16\)D) \(20\)E) \(24\)
8.
\(g(x)=f(x^2-1)\)
\(\Rightarrow g'(4)=?\)
A) \(8\cdot f'(4)\)B) \(2\cdot f'(4)\)C) \(8\cdot f'(15)\)D) \(8\cdot f'(16)\)E) \(4\cdot f'(15)\)