Here you can see the derivative f'(x) and the second derivative f''(x) of some common functions.Notice how the slope of each function is the y-value of the derivative plotted below it.For example, move to where the sin(x) function slope flattens out (slope=0), then see that the...
Answer to: Find the second derivative of the following function: y = sin^2(x) + cos^3(x). By signing up, you'll get thousands of step-by-step...
Answer to: Find the derivative and second derivative of the function. f(x) = \sin (2x^2 + 3) By signing up, you'll get thousands of step-by-step...
Step 1: Find the first derivative f′(x)We start by differentiating f(x)=cos(2x). Using the chain rule, we know that the derivative of cos(u) is −sin(u) multiplied by the derivative of u with respect to x. Here, u=2x. f′(x)=ddx(cos(2x))=−sin(2x)⋅ddx(2x)=−...
Use the second derivative test where applicable: {eq}f(x) = \sin^2x - \cos^2x, (0,2 \pi){/eq} Relative Extrema The relative extreme values of a function are the values of a function calculated at its critical points, such that the derivative function c...
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The Order is the highest derivative (is it a first derivative? a second derivative? etc):Example: dydx + y2 = 5x It has only the first derivative dy dx , so is "First Order"Example: d2ydx2 + xy = sin(x) This has a second derivative d2y dx2 , so is "Second Order" or "...
Find the first and second derivative for f(x)=x2−9x2−4 Quotient Rule of Derivative: If the function is given into the following from: f(x)=uv Then, the derivative of the given function is: f′(x)=u′v−uv′v2 Where, u' and v' are the derivatives of u and...
By deriving integrability conditions for the Lagrangian densityf, examples of integrable Lagrangians expressible via elementary functions, Jacobi theta functions and dilogarithms are constructed. A link of second-order integrable Lagrangians to WDVV equations is established. Generalisations to 3D second-or...
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