derivatives with AboEl5yr

if $$f(x) = 7x^5-3x^2+8$$ the $f'(x)$ is:

A) $35x^4-6x$ B) $35x^5-6x$ C) $35x^4-3x$ D) $7x^4-6x$

if $$f(x) = x^5-2x^3-4x$$ find $f''(x)$

A) $20x^3-12x$ B) $20x^4−6x^2+4$ C) $60x2−12$ D) $20x^3-6x$

find the third derivative of: $$x^6-3x^4+2x$$

A) $120x^3-72x$ B) $30x^4-36x^2+2$ C) $360x^2-72$ D) $120x^4-72x$

differentiate $$f(x)=4x^3+\frac{2}{x^2}-\frac{5}{x}$$

A) $12x^2 - \frac{4}{x^3} + \frac{5}{x^2}$ B) $12x^2 - \frac{4}{x^3} + \frac{5}{x^2}$ C) $12x^2 - \frac{2}{x^3} + \frac{5}{x}$ D) $12x^2 - \frac{4}{x^2} + \frac{5}{x^2}$

if the velocity function of a particle is $$f(x)=\frac{x^3\sin x+e^x}{x^2}$$ 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) $\frac{(4x^3\cos x-x^4\sin x+e^x)x^2-2x(x^4\cos x+e^x)}{x^4}$ C) $\frac{(4x^3\sin x-x^4\cos x+e^x)x^2-2x(x^4\cos x+e^x)}{x^4}$ D) $\frac{(4x^3\cos x-x^4\sin x-e^x)x^2-2x(x^4\cos x+e^x)}{x^4}$

find the jerk (yes that is a real physics concept, google it) of the velocity function: $$f(x)=x^3e^x\sin x$$

A) $e^x\left[(6x+6x^2)\sin x+(6x^2+x^3)\cos x\right]$ B) $e^x\left[(6x+6x^2)\cos x-(6x^2+x^3)\sin x\right]$ C) $e^x\left[(6x+6x^2-x^3)\sin x+2(3x^2+x^3)\cos x\right]$ D) $e^x\left[(6x+6x^2+x^3)\sin x+2(3x^2+x^3)\cos x\right]$

if $$f(x) = \frac{x^2 \sin x - x \cos x}{x+1}$$ then $f'(x) =$

A) $\frac{(2x \sin x + x^2 \cos x - \cos x + x \sin x)(x+1) + (x^2 \sin x - x \cos x)}{(x+1)^2}$ B) $\frac{(2x \sin x + x^2 \cos x - \cos x + x \sin x)(x+1) - (x^2 \sin x - x \cos x)}{(x+1)^2}$ C) $\frac{(2x \cos x - x^2 \sin x - \cos x + x \sin x)(x+1) + (x^2 \sin x - x \cos x)}{(x+1)^2}$ D) $\frac{(2x \sin x + x^2 \cos x + \cos x - x \sin x)(x+1) + (x^2 \sin x - x \cos x)}{(x+1)^2}$

differentiate $$x^3 2^x \log x$$

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... differentiate: $$\frac{x^5 2^x \log x \cos x}{x^2+4}$$

A) $\frac{x^5 2^x \log x \cos x}{(x^2+4)^2} \left[ \left( \frac5x + \ln 2 + \frac{1}{x \log x \ln 10} + \tan x \right) (x^2+4) - 2x \right]$ B) $\frac{x^5 2^x \log x \cos x}{(x^2+4)^2} \left[ \left( \frac5x + \ln 10 + \frac{1}{x \log x \ln 2} + \tan x \right) (x^2+4) - 2x \right]$ C) $\frac{x^5 2^x \log x \cos x}{(x^2+4)^2} \left[ \left( \frac5x + \ln 2 + \frac{1}{x \log x \ln 10} + \sec^2 x \right) (x^2+4) - 2x \right]$ D) $\frac{x^5 2^x \log x \cos x}{(x^2+4)^2} \left[ \left( \frac5x + \ln 2 + \frac{1}{x \log x \ln 10} - \tan x \right) (x^2+4) - 2x \right]$

Find the second derivative of: $$g(x) = \frac{x^4 7^x \log x \sin x}{(x-2)^2}$$ (good luck)

A) $ g(x)\left[ \left( \frac4x+\ln7+\frac{1}{x\log x\,\ln10} +\cot x-\frac2{x-2} \right)^2 + \left( -\frac4{x^2} -\frac{1+\log x\,\ln10} {x^2\log^2x\,(\ln10)^2} -\csc x +\frac2{(x-2)^2} \right) \right] $ B) $ g(x)\left[ \left( \frac4x+\ln7+\frac{1}{x\log x\,\ln10} +\cot x-\frac2{x-2} \right) + \left( -\frac4{x^2} -\frac{1+\log x\,\ln10} {x^2\log^2x\,(\ln10)^2} -\csc^2x +\frac2{(x-2)^2} \right) \right] $ C) $ g(x)\left[ \left( \frac4x+\ln7+\frac{1}{x\log x\,\ln10} +\cot x-\frac2{x-2} \right)^2 + \left( -\frac4{x^2} -\frac{1+\log x\,\ln10} {x^2\log^2x\,(\ln10)^2} -\csc^2x +\frac2{(x-2)^2} \right) \right] $ D) $ g(x)\left[ \left( \frac4x+\ln10+\frac{1}{x\log x\,\ln10} +\cot x-\frac2{x-2} \right)^2 + \left( -\frac4{x^2} -\frac{1+\log x\,\ln10} {x^2\log^2x\,(\ln10)^2} -\csc^2x +\frac2{(x-2)^2} \right) \right] $

Unit Test 2: Differentiation I