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.
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