Mathematics: What is the derivative of 5x^4+4?

X= 44 – y is the right equation....

What is the derivative of 5x^4+4?

Ответ:

fabiolafrancklin10

09.09.2021

Mathematics

$\displaystyle \frac{dy}{dx} = 20x^3$

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

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = 5x^4 + 4$

Step 2: Differentiate

Derivative Property [Addition/Subtraction]: $\displaystyle y' = \frac{d}{dx}[5x^4] + \frac{d}{dx}[4]$ Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle y' = 5\frac{d}{dx}[x^4] + \frac{d}{dx}[4]$ Basic Power Rule: $\displaystyle y' = 20x^3$

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

Unit: Differentiation

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What is the derivative of 5x^4+4?

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