Question
Which of the following expressions can be differentiated using the product rule?
A. \(arcsin(cosx)\)
B. \(sinx(arccosx)\)
C. \(e^x+arctanx\)
D. \((12x^2+3x−6)^e\)
Answer/Explanation
Ans:B
Question
Which of the following requires the use of implicit differentiation to find \(\frac{dy}{dx}\) ?
A \(2y+3x^2−x=5\)
B \(y=e^3+x+x^3\)
C \(y=e^{y+x}+x^3\)
D \(y=\frac{x^4+3}{4x^3−2}\)
Answer/Explanation
Ans: C
Question
For which of the following functions would the quotient rule be considered the best method for finding the derivative?
A \(y=(x^3+x)^{−2}\)
B \(y=\frac{x^3+x}{x}\)
C \(y=cos^{−1}(x^3+x)\)
D \(y=\frac{cos(x^3+x)}{x^3+x}\)
Answer/Explanation
Ans:D
Question
For \(0< x< \frac{\pi }{2}, ~if ~y = (sinx)^{x}, ~then~\frac{dy}{dx}\) is
(A)\(xln (sinx) \)
(B)\((sinx)^{x}cotx\)
(C)\(x(sinx)^{x-1}(cosx)\)
(D)\((sinx)^{x}(xcosx+sinx) \)
(E)\((sinx)^{x}(xcotx+In(sinx))\)