 # 5 Calculus Problems And Their Solutions

## Transcribed Text

1. If 𝑓(𝑥) = 𝑒5𝑥 Find the 8th derivative𝑓(8) (𝑥). (Hint: Find 𝑓′ (𝑥), 𝑓′′ (𝑥),etc. and look for a pattern) 𝑓(8) (𝑥) =? 2. Find the slope of the tangent line to the graph of the function 𝑓(𝑥) = 𝑥𝑒𝑥 At 𝑥 = 3 correct to two decimal places. The slope is:? 3. Find the derivative with respect to x of 𝑓(𝑥) = (𝑥 + 5)𝑒8𝑥+9. 𝑓′ (𝑥) =? 4. If 𝑓(𝑥) = ln(𝑥4 + 1) Find 𝑓′(7), correct to at least four decimal places. 𝑓′ (7) =? 5. If 𝑓(𝑥) = ln(ln(x)) Find 𝑓′(3), correct to at least four decimal places 𝑓′ (3) =?

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