Q&A for How to Calculate a Basic Derivative of a Function

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How do I know if a piecewise function is continuous?

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Expert Answer

In the context of a piecewise function, continuity is achieved when, from both the right and left approaches, the function values (f of X or Y) coincide at a specific X value. In simpler terms, the functions smoothly connect, and there is mutual agreement that a particular X value yields the same result for both functions. However, the differentiability of the piecewise function is contingent on whether the derivatives concur in terms of the values approached from both sides.

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What is the derivative of y=x^2 -2x+4?

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For a polynomial like this, the derivative of the function is equal to the derivative of each term individually, then added together. The derivative of x^2 is 2x. The derivative of -2x is -2. The derivative of any constant number, such as 4, is 0. Put these together, and the derivative of this function is 2x-2.

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How can I find the function if I know its derivative?

Pimemorized

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To find the original function again, you would integrate the function, which is the opposite of differentiating it.

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What is the function f(x) such that d/dx f(x) = f(x)?

Venatrixx

Community Answer

The function e^x has this property, where the derivative of the function is the same as the function. d/dx e^x = e^x

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What is the derivative of p(x)= -1/3x^2?

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The derivative of a constant times a power of x, is the same as the constant times the derivative of the power of x. We will use this rule to separate the constant this way d/dx(-1/3 * x²) = -1/3 * d/dx(x²). The derivative of x² is 2x⁽²⁻¹⁾ = 2x¹, so the answer is -1/3*2x = (-2/3)*x = -2x/3.

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