Example Question - derivative formula
Here are examples of questions we've helped users solve.
Derivative of a Quadratic Function using Power Rule
To find the derivative of the function y = x^2 with respect to x, you can use the power rule. The power rule states that for any function y = x^n, where n is a constant, the derivative, dy/dx, is given by n*x^(n-1). Applying the power rule to y = x^2: dy/dx = 2*x^(2-1) = 2*x So, the derivative of y = x^2 is dy/dx = 2x.
Derivative Calculation for a Function
The function f(x) provided in the image is: f(x) = (3x^5 - x^5) / 18x To differentiate this function, let's first simplify the expression f(x) by combining like terms in the numerator: f(x) = (3x^5 - x^5) / 18x = (2x^5) / 18x = (1/9)x^4 Now that we have the simplified form of f(x), we can differentiate it with respect to x: f'(x) = d/dx [(1/9)x^4] = (1/9) * d/dx [x^4] = (1/9) * (4x^3) Therefore, f'(x) = (4/9)x^3 Hence, the derivative of the function f(x) is (4/9)x^3 and is differentiable everywhere except at x = 0, since the original function included a term in the denominator with x, which would not be defined for x = 0.
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