4.4 Exponential Derivatives Recap!

​4.4 Exponential Derivatives Practice

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2. ​If needed, watch the video on the next slide to review finding exponential derivatives. ​

3. Complete the practice problems.

4. Turn in the completed worksheet. ​

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Multiple Choice

Find the derivative:

$$f\left(x\right)=e^{-4x}$$  

• $$f'\left(x\right)=4e^{4x}$$  

• $$f\left(x\right)=\frac{4}{e^{4x}}$$  

• $$f\left(x\right)=-4e^{4x}$$  

• $$f\left(x\right)=\frac{-4}{e^{4x}}$$  

Multiple Choice

Find the derivative:

$$f\left(x\right)=6^{5x}$$  

• $$f'\left(x\right)=5\cdot6^{5x}\ln6$$  

• $$f'\left(x\right)=30^{5x}\ln6$$  

• $$f'\left(x\right)=5\cdot6^{5x}$$  

• $$f'\left(x\right)=6^{5x}\ln6$$  

Multiple Choice

Find the derivative:

$$f\left(x\right)=5e^{x^3+1}$$  

• $$f'\left(x\right)=5e^{x^3+1}$$  

• $$f'\left(x\right)=15x^2e^{x^3+1}\ln5$$  

• $$f'\left(x\right)=15x^2e^{x^3+1}$$  

• $$f'\left(x\right)=5x^3e^{x^3+1}$$  

Multiple Choice

Find the derivative:

$$f\left(x\right)=7^{-x}$$  

• $$f'\left(x\right)=\frac{\ln7}{7^x}$$  

• $$f'\left(x\right)=\frac{-\ln7}{7^x}$$  

• $$f'\left(x\right)=-7^x\ln7$$  

• $$f'\left(x\right)=7^x\ln7$$  

Multiple Choice

Find the derivative:

$$f\left(x\right)=\frac{3^x}{e^x}$$  

• $$f'\left(x\right)=\frac{3^x\left(\ln3-1\right)}{e^2}$$  

• $$f'\left(x\right)=\frac{3^x\left(\ln3-1\right)}{e^x}$$  

• $$f'\left(x\right)=\frac{3^x\ln3}{e^x}$$  

• $$f'\left(x\right)=\frac{3^x\ln3}{e^{2x}}$$  

Multiple Choice

Find the derivative:

$$f\left(x\right)=5^xe^{-2x}$$  

• $$f'\left(x\right)=\frac{5^x\ln5}{e^{2x}}$$  

• $$f'\left(x\right)=-2\cdot5^xe^{-2x}\ln5$$  

• $$f'\left(x\right)=\frac{-2\cdot5^x\ln5}{e^{2x}}$$  

• $$f'\left(x\right)=\frac{-5^x\left(\ln5+2\right)}{e^{2x}}$$  

Multiple Choice

Find the derivative:

$$f\left(x\right)=5x^2e^x$$  

• $$f'\left(x\right)=10xe^x$$  

• $$f'\left(x\right)=5xe^x\left(x+2\right)$$  

• $$f'\left(x\right)=5x\left(xe^x-2\right)$$  

• $$f'\left(x\right)=10xe^x+2$$  

Multiple Choice

Find the derivative:

$$f\left(x\right)=\frac{3x^2}{4^x}$$  

• $$f'\left(x\right)=\frac{6x}{4^x\ln4}$$  

• $$f'\left(x\right)=\frac{3x\left(2-x\ln4\right)}{16}$$  

• $$f'\left(x\right)=\frac{3x\left(2-x\ln4\right)}{4^x}$$  

• $$f'\left(x\right)=\frac{6x-4^x\ln4}{\ln4}$$  

Multiple Choice

Find the derivative:

$$f\left(x\right)=3e^{\cos\left(4x\right)}$$  

• $$f'\left(x\right)=12e^{\sin\left(4x\right)}$$  

• $$f'\left(x\right)=-3\sin\left(4x\right)e^{\cos\left(4x\right)}$$  

• $$f'\left(x\right)=-12\sin\left(4x\right)e^{\cos\left(4x\right)}$$  

• $$f'\left(x\right)=-12e^{\cos\left(4x\right)}$$  

Multiple Choice

Find the derivative:

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

• $$f'\left(x\right)=\frac{e^x\left(x+1\right)}{2^x\ln2}$$  

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

• $$f'\left(x\right)=\frac{2^xe^x\left(2\ln2-1\right)}{2^{2x}}$$  

• $$f'\left(x\right)=\frac{e^x\left(x+1-x\ln2\right)}{2^x}$$  

Open Ended

How do you feel about finding the derivative of exponential functions?