AP Calculus AB: 2.7 Derivatives of cos x, sin x, ex, and ln x

If $f(x)=\ln x$,then $\lim_{x\rightarrow 3}\frac{f(x)-f(3)}{x-3}$

A $\frac{1}{3}$

B $e^{3}$

C ln 3

D non existent

▶️Answer/Explanation

Ans: A

If ln(2x+y)=x+1,then $\frac{\mathrm{d} y}{\mathrm{d} x}$=

A -2

B 2x+y−2

C 2x+y

D 4x+2y−2

E $y-\frac{y}{x}$

▶️Answer/Explanation

Ans:B

If $f(x)=e^{x}$,then $\ln (f{}'(2))$=

A 2

B 0

C $\frac{1}{e^{2}}$

D 2e

E $e^{2}$

▶️Answer/Explanation

Ans:A

$\frac{\mathrm{d} }{\mathrm{d} x}(2^{x})$=

A $2^{x-1}$

B $(2^{x-1})x$

C $(2^{x})\ln 2$

D $(2^{x-1})\ln 2$

E $\frac{2x}{\ln 2}$

▶️Answer/Explanation

Ans:C

AP Calculus AB: 2.7 Derivatives of cos x, sin x, ex, and ln x – Exam Style questions with Answer- MCQ