$$\frac{\text{d}y}{\text{d}x}=2\sin2x$$

$$\frac{\text{d}y}{\text{d}x}=-2\sin2x$$

$$\frac{\text{d}y}{\text{d}x}=-\sin\left(-2x\right)$$

$$\frac{\text{d}y}{\text{d}x}=2\sin\left(-2x\right)$$

$$f'\left(x\right)=\frac{e^{\frac{x}{2}}}{2}$$

$$f'\left(x\right)=2e^{\frac{x}{2}}$$

$$f'\left(x\right)=\frac{e^{\frac{x}{2}}}{\frac{1}{2}}$$

$$f'\left(x\right)=e^{\frac{x}{2}}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{1}{\left(2+3x\right)}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{3}{\left(2+3x\right)}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{2}{\left(2+3x\right)}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{1}{3\left(2+3x\right)}$$

$$\frac{\text{d}y}{\text{d}x}=5xe^{2x}+5e^{2x}$$

$$\frac{\text{d}y}{\text{d}x}=10xe^{2x}+5e^{2x}$$

$$\frac{\text{d}y}{\text{d}x}=5xe^{2x}+10e^{2x}$$

$$\frac{\text{d}y}{\text{d}x}=10xe^{2x}+10e^{2x}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{6x^2+20x+3}{\left(3x+5\right)^2}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{18x^2+20x+3}{\left(3x+5\right)^2}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{-18x^2+20x-3}{\left(3x+5\right)^2}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{6x^2+20x-3}{\left(3x+5\right)^2}$$

$$f'\left(u\right)=6\left(\sin3t\right)^5$$

$$f'\left(u\right)=18\cos3t\left(\sin3t\right)^5$$

$$f'\left(u\right)=6\left(\cos3t\right)^5$$

$$f'\left(u\right)=18\cos t\left(3\sin t\right)^6$$

$$\frac{\text{d}y}{\text{d}x}=\frac{x-5}{y}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{-x}{y^2}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{-x}{y}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{-y}{x}$$

$$f''''\left(x\right)=e^{3x-1}$$

$$f''''\left(x\right)=108e^{3x}$$

$$f''''\left(x\right)=162e^{3x}$$

$$f''''\left(x\right)=216e^{3x-1}$$

$$\frac{d^2y}{\text{d}x^2}=1$$

$$\frac{d^2y}{\text{d}x^2}=6$$

$$\frac{d^2y}{\text{d}x^2}=12$$

$$\frac{d^2y}{\text{d}x^2}=24$$