Unit Test 3: Differentiation II

if $$y=(4x-1)^3$$ the $\frac{dy}{dx}$ is:

A) $3(4x−1)^2$ B) $2(4x−1)^3$ C) $4(4x−1)^2$ D) $12(4x−1)^2$

if $$y = \sqrt{5x^2 + 1}$$ find $\frac{dy}{dx}$

A) $\frac{5x}{5x^2-1}$ B) $\frac{10x}{2x^2-1}$ C) $\frac{x}{5x^2-1+5}$ D) $\frac{5}{x^2}$

$$y = sin(2x^3+1), \frac{dy}{dx} = ???$$

A) $6x^2 cos(2x^3+1) - 72x$ B) $sin(2x^3+1)$ C) $cos(6x^2+1)$ D) $6x^2 cos(2x^3+1)$

differentiate $$e^{(x^2-3x)}$$

A) $(2x-3)e^{(2x-3)}$ B) $(2x-3)e^{(x^2-3x)}$ C) $(2x-3)e$ D) $(2x-3)e^{(x^2+3x)}$

if the velocity function of a particle is $$f(x)= \ln(3x^2+4x+2)$$ find the acceleration

A) $\frac{(4x^3\cos x-x^4\sin x+e^x)x^2+2x(x^4\cos x+e^x)}{x^4}$ B) $\frac{6x+4}{3x^2+4x+2} e^{(6x+4)}$ C) $\frac{6x+4}{\ln(3x^2+4x+2)}$ D) $\frac{6x+4}{3x^2+4x+2}$

find the jerk (yes that is a real physics concept, google it) of the acceleration relation: $$x^2 + y^2 = 49$$

A) $-\frac xy$ B) $-\frac yx$ C) $\frac xy$ D) $\frac xy$

if $$f(x) = x^2 + xy + y^2 = 12$$ then $f'(x) =$

A) $-\frac{x+2y}{2x+y}$ B) $\frac{x+2y}{2x+y}$ C) $-\frac{2x+y}{x+2y}$ D) $\frac{2x+y}{x+2y}$

differentiate $$x^2 y + y^3 = 9$$

A) $x^2 2^x \left((x+3)\log x + \frac{1}{\ln 10}\right)$ B) $x^2 2^x \left((x \ln 2+3)\log x + \frac{1}{\ln 10}\right)$ C) $x^2 2^x \left((x+3)\ln x + \frac{1}{\ln 10}\right)$\) D) $x^2 2^x \left((x+3)log x + \frac{1}{\ln 20}\right)$

good luck with the next 2 problems, u will need it... find $\frac{dy}{dx}$ where: $$e^{xy} = x+y$$

A) $\frac{1-e^{xy}}{1-xe^{xy}}$ B) $\frac{ye^{x}-1}{1+xe^{y}}$ C) $\frac{xe^{xy}-1}{ye^{xy}}$ D) $\frac{ye^{xy}-1}{1-xe^{xy}}$

if: $$\sin(xy) +x^2 y = e^y$$

A) $\frac{e^y - 2xy - y \cos(xy)}{x \cos(xy) + x^2 -e^y}$ B) $\frac{e^y - xy - x \cos(xy)}{y \cos(xy) + x^2 -e^y}$ C) $\frac{x - 2x - e^y \cos(xy)}{x \cos(xy) + y^2 + e^y}$ D) $\frac{e^y - y \cos(y)}{x \cos(x) + x^2 - e^y}$