Question
If \(x^{2}+xy-3y=3\) then at the point (2, 1),\(\frac{\mathrm{d} y}{\mathrm{d} x}\)
A 5
B 4
C \(\frac{7}{3}\)
D 2
▶️Answer/Explanation
Ans:A
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
Ans:B
Question
If \(x^{2}+y^{2}=25\) what is the value of \(\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}\) at the point (4,3) ?
A \(-\frac{25}{27}\)
B \(-\frac{7}{27}\)
C \(\frac{7}{27}\)
D \(\frac{3}{4}\)
E \(\frac{25}{27}\)
▶️Answer/Explanation
Ans:A
Question
\(\frac{\mathrm{d} }{\mathrm{d} x}(x^{5}-5^{x})=\)
A \(\frac{x^{6}}{6}-\frac{5^{x}}{\ln 5}\)
B \(5x^{4}-5^{x}\)
C \(5x^{4}-x.5^{x-1}\)
D \(5x^{4}-(\ln 5) 5^{x}\)
▶️Answer/Explanation
Ans:D
The derivative of \(x^{5}\) is \(5x^{4}\) by the power rule, and the derivative of the exponential function \(5^{x}\) is (\ln 5)5^{x}\) Therefore,\(\frac{\mathrm{d} }{\mathrm{d} x}(x^{5}-5^{x})=5x^{4}-(\ln 5)5^{x}\)