Question

if d/dx f(x) = g(x) and if h(x) =x^2 then d/dx f(h(x)) = ?

Answer 1

Answer:

$\displaystyle \frac{d}{dx} f(h(x)) = g(x^2)2x$

General Formulas and Concepts:
Calculus

Differentiation

• Derivatives
• Derivative Notation

Derivative Rule [Basic Power Rule]:

1. f(x) = cxⁿ
2. f’(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

$\displaystyle \frac{d}{dx} f(x) = g(x)$

$\displaystyle h(x) = x^2$

Step 2: Differentiate

1. Derivative Rule [Chain Rule]:                                                                       $\displaystyle \frac{d}{dx} f(h(x)) = \frac{d}{dx} f(h(x)) \cdot \frac{d}{dx} h(x)$
2. [Derivative] Substitute in variables:                                                            $\displaystyle \frac{d}{dx} f(h(x)) = g(x^2) \cdot \frac{d}{dx} x^2$
3. Derivative Rule [Basic Power Rule]:                                                           $\displaystyle \frac{d}{dx} f(h(x)) = g(x^2)2x$

---

Learn more about derivatives: https://brainly.com/question/25804880

---

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

Unit: Differentiation