# 20 Lecture

## MTH101

### Midterm & Final Term Short Notes

## Derivative of Logarithmic and Exponential Functions

Logarithmic and exponential functions are widely used in mathematics and various other fields of study. In calculus, understanding how to differentiate these functions is crucial for solving complex problems.

**Important Mcq's**

Midterm & Finalterm Prepration

Past papers included

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**What is the derivative of ln(x)?**

a) x

b) 1/x

c) ln(x)

d) 0

Solution: b) 1/x

**What is the derivative of e^x?**

a) x

b) e^x

c) ln(x)

d) 0

Solution: b) e^x

**What is the derivative of ln(u), where u is a function of x?**

a) 1/u

b) u/ln(u)

c) u'/ln(u)

d) ln(u)/u'

Solution: c) u'/u

**What is the derivative of e^u, where u is a function of x?**

a) e^u

b) u'e^u

c) e^(u/x)

d) e^(u^2)

Solution: b) u'e^u

**What is the derivative of ln(ax), where a is a constant?**

a) 1/xln(a)

b) a/x

c) xln(a)

d) 0

Solution: a) 1/xln(a)

**What is the derivative of e^(ax), where a is a constant?**

a) ae^x

b) e^(ax)

c) x^a

d) a^x

Solution: a) ae^(ax)

**What is the derivative of ln(x^n), where n is a constant?**

a) nln(x)

b) n/x

c) x/n

d) 0

Solution: b) n/x

**What is the derivative of e^(nx), where n is a constant?**

a) e^(nx)

b) n^x

c) ne^(nx)

d) e^(n^x)

Solution: c) ne^(nx)

**What is the derivative of ln(e^x)?**

a) x

b) 1

c) e^x

d) ln(x)

Solution: b) 1

**What is the derivative of e^(ln(x))?**

a) x

b) e^x

c) ln(x)

d) 1

Solution: a) x

**Subjective Short Notes**

Midterm & Finalterm Prepration

Past papers included

Download PDF
**What is the derivative of ln(x)?**

**Answer: **The derivative of ln(x) is 1/x.

**What is the derivative of e^x?**

**Answer:** The derivative of e^x is e^x.

**What is the derivative of ln(u), where u is a function of x?**

**Answer: **The derivative of ln(u) is u'/(u).

**What is the derivative of e^u, where u is a function of x?**

**Answer:** The derivative of e^u is e^u * u'.

**What is the derivative of ln(ax), where a is a constant?**

**Answer:** The derivative of ln(ax) is 1/(xln(a)).

**What is the derivative of e^(ax), where a is a constant?**

**Answer:** The derivative of e^(ax) is ae^(ax).

**What is the derivative of ln(x^n), where n is a constant?**

**Answer: **The derivative of ln(x^n) is n/x.

**What is the derivative of e^(nx), where n is a constant?**

**Answer:** The derivative of e^(nx) is ne^(nx).

**What is the derivative of ln(e^x)?**

**Answer:** The derivative of ln(e^x) is 1.

**What is the derivative of e^(ln(x))?**

**Answer: **The derivative of e^(ln(x)) is x.