Mathematics: Find the derivative of log[10x+7] by first principle

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Find the derivative of log[10x+7] by first principle

Ответ:

mazielynn84

09.02.2022

Mathematics

$\displaystyle y' = \frac{10}{(10x + 7) \ln 10}$

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = \log (10x + 7)$

Step 2: Differentiate

Logarithmic Differentiation [Derivative Rule - Chain Rule]: $\displaystyle y' = \frac{(10x + 7)'}{(10x + 7) \ln 10}$ Basic Power Rule [Derivative Properties]: $\displaystyle y' = \frac{10}{(10x + 7) \ln 10}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

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Find the derivative of log[10x+7] by first principle

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