Question
\(\frac{\mathrm{d} }{\mathrm{d} x}(x^{3}\sec (2x))\)=
A \(6x^{2}\sec (2x)\tan (2x)\)
B \(2x^{3}\tan ^{2}(2x)+3x^{2} \sec (2x)\)
C \(x^{3}\sec (2x)\tan (2x)+3x^{2}\sec (2x)\)
D \(2x^{3}\sec (2x)\tan (2x)+3x^{2}\sec (2x)\)
▶️Answer/Explanation
Ans:D
Question
\(\frac{\mathrm{d} }{\mathrm{d} x}(2(\sin \sqrt{x})^{2})\)
A \(4\cos (\frac{1}{2\sqrt{2}})\)
B \(4\sin \sqrt{x}\cos \sqrt{x}\)
C \(\frac{2\sin \sqrt{x}}{\sqrt{x}}\)
D \(\frac{2\sin \sqrt{x}\cos \sqrt{x}}{\sqrt{x}}\)
▶️Answer/Explanation
Ans:D
Question
If f is a differentiable function and \(y=\sin (f(x^{2}))\) what is \(\frac{\mathrm{d} y}{\mathrm{d} x}\) when x = 3 ?
A \(\cos (f{}'(9))\)
B \(6\cos (f{}(9))\)
C \(f{}'(9)\cos (f(9))\)
D \(6f{}'(9)\cos (f(9))\)
▶️Answer/Explanation
Ans:D
Question
If \(f(x)=\sin (x^{2}+\pi )\) ,then \(f{}'(\sqrt{2\pi })\)
A \(-2\sqrt{2\pi }\)
B -2
C -1
D \(\cos (2\sqrt{2})\)
▶️Answer/Explanation
Ans:A