Pregunta: In problems 1−14, find the derivative: 1. f(x)=2x−5x2−3 2. f(x)=excosx 3. y=tan(ln(2x+1)) 4. y=cos4(x2) 5. y=1+sinxcosx 7. f(x)=ln(1+ex) 8. f(x)=e−2x2 9. y=(1−cosx1+sinx)2 10. y=sin(x2) 11. y=x2x+1 12y=2x3.5+x−3.5+tan(3.5x)+3.52 13. y=secxtanx 14. y=1+cosx 15. Find the derivative of y=hfg, in terms of f,g,h,f′,g′, and h′, where f,g, and h are functions of x.

In problems $1-14$, find the derivative: 1. $f(x)=\frac{x^2-3}{2x-5}$ 2. $f(x)=e^x\cos x$ 3. $y=\tan (\ln (2x+1))$ 4. $y={\cos }^4\left(x^2\right)$ 5. $y=\frac{\cos x}{1+\sin x}$ 7. $f(x)=\ln \left(1+e^x\right)$ 8. $f(x)=e^{-\frac{x^2}{2}}$ 9. $y={\left(\frac{1+\sin x}{1-\cos x}\right)}^2$ 10. $y=\sin \left(\frac{2}{x}\right)$ 11. $y=x\sqrt{2x+1}$ $12y=2x^{3.5}+x^{-3.5}+\tan (3.5x)+3.5^2$ 13. $y=\sec x\tan x$ 14. $y=\sqrt{1+\cos x}$ 15. Find the derivative of $y=\frac{fg}{h}$, in terms of $f,g,h,f^{\prime },g^{\prime }$, and $h^{\prime }$, where $f,g$, and $h$ are functions of $x$. 16. Find the rate of change of $y={\left(4x^3+7x^2+1\right)}^2$ at $x=-1$. 17. If $f(x)={\sin }^{3}x$, find $f^{\prime \prime }(x)$ 18. Find the slope of the line tangent to the curve $y=\cos (2x)$ at the point where $x=\frac{\pi }{6}$. 19. Let $f(x)=\{\begin{array}{l}\sin (\pi x),0\le x\le 1\\ ax+b,1<x\le 2\end{array}$. Find the values of $a$ and $b$ such that $f(x)$ is differentiable at $x=1$. 20. Which of the following functions are NOT differentiable at $x=0$ ? I. $y=\sqrt{4-x^2}$ II. $y=x^{2/3}$ III. $y=x^{4/3}$ IV. $y=x^{-2}$ V. $y=|\sin (2x)|$