Sum rule of differentiation Calculator

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Example

Created on 2024-06-20Asked by Aria Martin (Solvelet student)

Differentiate

f(x) = 3x^2 + 5x + 7

Solution

To differentiate

f(x) = 3x^2 + 5x + 7

: 1. **Apply the sum rule:**

\frac{d}{dx}(3x^2 + 5x + 7) = \frac{d}{dx}(3x^2) + \frac{d}{dx}(5x) + \frac{d}{dx}(7).

2. **Differentiate each term:**

\frac{d}{dx}(3x^2) = 6x, \quad \frac{d}{dx}(5x) = 5, \quad \frac{d}{dx}(7) = 0.

3. **Combine the results:**

f'(x) = 6x + 5.

4. **Result:** The derivative of

f(x)

6x + 5

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Isabella Anderson on Solvelet

1. Differentiate the function

f(x) = x^2 + 3x - 2

with respect to

x

.2. Find the derivative of the function

g(x) = \sin(x) + \ln(x)

with respect to

x

DefinitionSum rule of differentiation: If f and g are both differentiable at x, then the function h defined by h(x) = f(x) + g(x) is also differentiable at x and we have h'(x) = f'(x) + g'(x) For example, (f+g)′(x)=f′(x)+g′(x) if f(x),g(x) are differentiable. Example: The sum of the functions f(x)=x2 and g(x)=3x is f(x)+g(x)=x2+3x, and its derivatives are 2x+3.

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