Question
Given that 3x − tan y = 4, what is \(\frac{\mathrm{d} y}{\mathrm{d} x}\) in terms of y?
A \(\frac{\mathrm{d} y}{\mathrm{d} x}=3\sin ^{2}y\)
B \(\frac{\mathrm{d} y}{\mathrm{d} x}=3\cos ^{2}y\)
C \(\frac{\mathrm{d} y}{\mathrm{d} x}=3\cos y\cot y\)
D \(\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{3}{1+9y^{2}}\)
Answer/Explanation
Question
\(\frac{\mathrm{d} }{\mathrm{d} x}(\cot x)\)=
A −tanx
B \(\sec ^{2}x\)
C tanx
D \(-\csc ^{2}x\)
Answer/Explanation
Question
\(\frac{\mathrm{d} }{\mathrm{d} x}(\sin x\csc x)=\)
A 0
B 1
C \(-\cot ^{2}x\)
D 2cotx
Answer/Explanation
Ans:A
Question
Below is an attempt to derive the derivative of cscx using the product rule, where x is in the domain of cscx. In which step, if any, does an error first appear?
Step 1: cscx⋅sinx=1
Step 2: \(\frac{\mathrm{d} }{\mathrm{d} x}(\csc x.\sin x)=0\)
Step 3:\(\frac{\mathrm{d} }{\mathrm{d} x}(\csc x).\sin x+\csc x.\cos x=0\)
Step 4:\( \frac{\mathrm{d} }{\mathrm{d} x}(\csc x)=\frac{-\csc x.\cos x}{\sin x}=-\csc x.\cot x\)
A Step 1
B Step 2
C Step 3
D There is no error.
Answer/Explanation
Ans:D