How to Find the Derivative of a Polynomial Function: Power Rule Explained with Example

find derivative of f(x)= 2x^10-4x²?

To find the derivative of the function f(x) = 2x^10 – 4x^2, we can use the power rule of differentiation

To find the derivative of the function f(x) = 2x^10 – 4x^2, we can use the power rule of differentiation. According to the power rule, if we have a term of the form x^n, the derivative is obtained by multiplying the coefficient (n) by the exponent (n-1) and also keeping x to the power of (n-1).

Applying the power rule to each term in the given function, we get:

f'(x) = d/dx (2x^10) – d/dx (4x^2)

For the first term, d/dx (2x^10), the coefficient is 2 and the exponent is 10. Applying the power rule, we obtain:

f'(x) = 2 * 10x^(10-1) – d/dx (4x^2)

Simplifying further, we have:

f'(x) = 20x^9 – d/dx (4x^2)

For the second term, d/dx (4x^2), the coefficient is 4 and the exponent is 2. Applying the power rule, we get:

f'(x) = 20x^9 – 4 * 2x^(2-1)

Simplifying further:

f'(x) = 20x^9 – 8x

Therefore, the derivative of the function f(x) = 2x^10 – 4x^2 is f'(x) = 20x^9 – 8x.

More Answers:

Derivative of the function f(x) = x² + 3x – 6 using the power rule
Power Rule: How to Find the Derivative of a Quadratic Function – Step by Step Guide
Maximizing Efficiency: Finding and Applying the Derivative using the Quotient Rule

Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded

Share:

Recent Posts

Mathematics in Cancer Treatment

How Mathematics is Transforming Cancer Treatment Mathematics plays an increasingly vital role in the fight against cancer mesothelioma. From optimizing drug delivery systems to personalizing

Read More »