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The first derivative f'(x) gives the instantaneous slope of f(x). If f'(x) is positive, then f(x) is increasing (positive slope), and if f'(x) is negative, then f(x) is decreasing (negative slope). If f'(x) = 0, then the graph of f(x) is flat at the point (slope = 0).

Q: What is the first derivative used for?

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Yes.

The first derivative of ln x is 1/x, which (for the following) you better write as x-1.Now use the power rule:Second derivative (the derivative of the first derivative) is -1x-2, the third derivative is the derivative of this, or 2x-3. You may now wish to write this in the alternative form, as 2 / x3.

well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.

The first derivative is the rate of change, and the second derivative is the rate of change of the rate of change.

in case of derivative w.r.t time first derivative with a variable x gives velocity second derivative gives acceleration thid derivative gives jerk

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All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2

Speed is scalar (it doesn't have direction), and the magnitude of velocity (a vector). The first derivative of velocity is acceleration, therefore the first derivative of speed is the magnitude of acceleration.

sobel is the first derivative method that is used to detect edges,, while laplace method is the 2nd derivative method that is used to detect the change of slope.

2x is the first derivative of x2.

2x is the first derivative of x2.

Yes.

Afetr you take the first derivative you take it again Example y = x^2 dy/dx = 2x ( first derivative) d2y/dx2 = 2 ( second derivative)

The first derivative of ln x is 1/x, which (for the following) you better write as x-1.Now use the power rule:Second derivative (the derivative of the first derivative) is -1x-2, the third derivative is the derivative of this, or 2x-3. You may now wish to write this in the alternative form, as 2 / x3.

well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.

The first derivative is the rate of change, and the second derivative is the rate of change of the rate of change.

in case of derivative w.r.t time first derivative with a variable x gives velocity second derivative gives acceleration thid derivative gives jerk

A linear function, for example y(x) = ax + b has the first derivative a.