Problems on Derivatives of Exponential Function Part 4 - Derivatives - Diploma Maths - II | Summary and Q&A

TL;DR

Learn how to solve the derivative of exponential functions with step-by-step examples.

Key Insights

• 🍉 Differentiating exponential functions involves differentiating each term separately.
• 🤶 The derivative of e^MX is M*e^MX, where M is a constant.
• ❓ The derivative of a constant function is always 0.
• ✖️ Algebraic functions can be differentiated by multiplying the original exponent by the coefficient and subtracting 1.
• 🗂️ The derivative of the natural logarithm of a function is 1 divided by the function itself, multiplied by the derivative of the function.
• 📏 Differentiating exponential functions requires applying the product rule and chain rule.
• ❓ The exponential function e^X has a derivative of e^X.

Transcript

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Questions & Answers

Q: How do you find the derivative of an exponential function?

To find the derivative of an exponential function, differentiate each term separately. The derivative of e^MX is M*e^MX, where M is a constant.

Q: How do you differentiate a constant function?

The derivative of a constant function is always 0, as the rate of change is zero.

Q: How do you differentiate an algebraic function like X^5?

To differentiate an algebraic function, multiply the original exponent by the coefficient, and subtract 1 from the original exponent.

Q: What is the derivative of log functions?

The derivative of the natural logarithm of a function is 1 divided by the function itself, multiplied by the derivative of the function.

Summary & Key Takeaways

• The video demonstrates how to find the derivative of exponential functions through two example problems.

• In problem number 8, it shows how to differentiate the function Y = AE^MX + BY^-MX.

• In problem number 9, it explains how to differentiate the function Y = Phi^X + X^5 + e^5 - log(Phi)e.