Chain Rule, Implicit, Logs and Exponential Derivatives

 $x^2\left(\ln3\right)\left(3^{x^2-1}\right)$  

 $\left(\ln3\right)\left(3^{x^2-1}\right)$  

 $\left(2x\right)\left(3^{x^2-1}\right)$  

 $2x\left(\ln3\right)\left(3^{x^2-1}\right)$  

 $\left(\cos\sqrt{x}\right)e^{\sin\sqrt{x}}$  

 $\frac{e^{\cos\sqrt{x}}}{2\sqrt{x}}$  

 $\frac{\cos\sqrt{x}}{2\sqrt{x}}\left(e^{\sin\sqrt{x}}\right)$  

 $\left(\sin\sqrt{x}\right)e^{\left(\sin\sqrt{x}-1\right)}$  

 $\frac{1}{2\sqrt{2e^{2x}}}$  

 $\frac{e^{2x}}{\sqrt{5+e^{2x}}}$  

 $\frac{5+e^{2x}}{\sqrt{5+e^{2x}}}$  

 $\frac{xe^{\left(2x-1\right)}}{\sqrt{5+e^{2x}}}$  

 $\left(\sec^{-1}\left(\cos\ x\right)\right)^2$  

 $\frac{1}{\left(\cos^{-1}x\right)^2+1}$  

 $-\left(\sec^{-1}\left(\cos x\right)\right)^2\sin x$  

 $\frac{-\sin x}{1+\cos^2x}$  

1/7

1/35

7

35

 $\cos^3\left(4x\right)$  

 $3\sin^2\left(4x\right)\cos\left(4x\right)$  

 $12\sin^2\left(4x\right)\cos\left(4x\right)$  

 $4\cos^3\left(4x\right)$  

x = 0 only

x = 0 and x = - 4

x = - 4 only

x = - 4, x = 0, and x = 4

 $6x\left(x^2-2\right)^2$  

 $6x\left(x+1\right)\left(x^2-2\right)^2$  

 $3\left(x+1\right)\left(x^2-2\right)^2$  

 $\left(x^2-2\right)^2\left(7x^2+6x-2\right)$  

 $2\left(\cos\ x^2-x\sin x^2\right)$  

 $2\left(\cos x^2-2x^2\sin x^2\right)$  

 $2x\cos x^2$  

 $-4x\sin x^2$  

5/2

-2/3

-5/3

-15/2