DBM20023 Exponential Differentiation

$$\frac{\text{d}y}{\text{d}x}=2xe^{3-x^2}$$  

$$\frac{\text{d}y}{\text{d}x}=-2xe^{3-x^2}$$  

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

$$\frac{\text{d}y}{\text{d}x}=-x^2e^{3-x^2}$$  

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

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

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

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

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

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

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

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

$$\frac{\text{d}y}{\text{d}x}=3e^{3x}+5e^{-x}$$  

$$\frac{\text{d}y}{\text{d}x}=3e^{3x}-5e^{-x}$$  

$$\frac{\text{d}y}{\text{d}x}=3e^{3x}+5e^x$$  

$$\frac{\text{d}y}{\text{d}x}=3e^{3x}+5e^{-4x}$$  

$$\frac{\text{d}y}{\text{d}x}=3x^2\left(e^{4x-1}\right)\left(3-4x\right)$$  

$$\frac{\text{d}y}{\text{d}x}=3x^2\left(e^{4x-1}\right)\left(3+4x\right)$$  

$$\frac{\text{d}y}{\text{d}x}=\left(e^{4x-1}\right)\left(3+4x\right)$$  

$$\frac{\text{d}y}{\text{d}x}=3x^2+\left(e^{4x-1}\right)$$  

$$\frac{\text{d}y}{\text{d}x}=9e^{-3x}+2e^{2x}$$  

$$\frac{\text{d}y}{\text{d}x}=9e^{-3x}-2e^{2x}$$  

$$\frac{\text{d}y}{\text{d}x}=-9e^{-3x}-2e^{2x}$$  

$$\frac{\text{d}y}{\text{d}x}=-9e^{-3x}+2e^{2x}$$  

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

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

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

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

$$\frac{\text{d}}{\text{d}x}=4e^{5x}\left(1+e^{5x}\right)^3$$  

$$\frac{\text{d}}{\text{d}x}=20e^{5x}\left(1+e^{5x}\right)^3$$  

$$\frac{\text{d}}{\text{d}x}=5e^{5x}\left(1+e^{5x}\right)^3$$  

$$\frac{\text{d}}{\text{d}x}=20e^{5x}\left(1+e^{5x}\right)$$  

$$\frac{\text{d}y}{\text{d}x}=-3e^{-3x+1}$$  

$$\frac{\text{d}y}{\text{d}x}=3e^{1-3x}$$  

$$\frac{\text{d}y}{\text{d}x}=3e^{3x+1}$$  

$$\frac{\text{d}y}{\text{d}x}=-3xe^{-3x+1}$$  

$$\frac{\text{d}y}{\text{d}x}=7e^{7x}$$  

$$\frac{\text{d}y}{\text{d}x}=-7e^{7x}$$  

$$\frac{\text{d}y}{\text{d}x}=\frac{e^{7x}}{7}$$  

$$\frac{\text{d}y}{\text{d}x}=7xe^{7x}$$