Question
If \(\frac{\mathrm{d} y}{\mathrm{d} x}=x^{4}-2x^{3}+3x-1\), then \(\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}\) evaluated at x=2 is
A 11
B 24
C 26
D 125
▶️Answer/Explanation
Ans:B
Question
If \(y=e^{x^{3}}\),then \(\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}\)
A \(18x^{3}e^{x^{3}}\)
B \(9x^{4}e^{2x^{3}}\)
C \((6x+3x^{2})e^{x^{3}}\)
D \(9(6x+9x^{4})e^{x^{2}}\)
▶️Answer/Explanation
Ans:D
Question
If \(y=e^{2\sin x}\),then \(\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}\)
A \((4\cos ^{2}x)(e^{4\sin x})\)
B \((-4\sin x\cos x)(e^{2\sin x})\)
C \((-\sin x+\cos x)(2e^{2\sin x})\)
D \((-\sin x+2\cos ^{2}x)(2e^{2\sin x})\)
▶️Answer/Explanation
Ans:D
Question
If \(y=-3\cos (2x)\) , then \(\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}\)
A −12cos(2x)
B 12cos(2x)
C −3cos(2x)
D 3cos(2x)
▶️Answer/Explanation
Ans:B
The chain rule must be used twice to find the second derivative
\(\frac{\mathrm{d} Y}{\mathrm{d} x}=-3(-\sin (2x)).2\)
\(\frac{\mathrm{d}^{2} y}{\mathrm{d} x^{2}}=\frac{\mathrm{d} }{\mathrm{d} x}(6\sin (2x)).2=12\cos 2x\)