DERIVATIVE OF A GENERAL LOGARITHMIC FUNCTION

Solved Problems

Find ᵈʸ⁄dₓ in each of the following.

Problem 1 :

y = log₆x

Solution :

y = log₆x

Problem 2 :

y = log₁₀(2x)

Solution :

Method 1 :

y = log₁₀(2x)

Method 2 :

y = log₁₀(2x)

Use the product rule of logarithm.

y = log₁₀2 + log₁₀x

Problem 3 :

y = log₅(3x²)

Solution :

Method 1 :

y = log₅(3x²)

Method 2 :

y = log₅(3x²)

Use the product rule of logarithm.

y = log₅3 + log₅x²

Use the power rule of logarithm.

y = log₅3 + 2log₅x

Problem 4 :

y = log₁₀√x

Solution :

Method 1 :

y = log₁₀√x

Method 2 :

y = log₁₀√x

y = log₁₀x^½

Use the power rule of logarithm.

Problem 5 :

y = log₁₀e^x

Solution :

Method 1 :

y = log₁₀e^x

Method 2 :

y = log₁₀e^x

Use the power rule of logarithm.

y = xlog₁₀e

Problem 6 :

y = log₂(3x² + 5x - 8)

Solution :

y = log₂(3x² + 5x - 8)

Problem 7 :

y = log₇(sinx)

Solution :

y = log₇(sinx)

Problem 8 :

y = log₄(cosx)

Solution :

y = log₄(cosx)

Problem 9 :

y = log₉(tanx)

Solution :

y = log₉(tanx)

Problem 10 :

y = log₅(sin√x)

Solution :

y = log₅(sin√x)

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