By one of the trigonometric identities, sin2y + cos2y = 1. From this, cos y = √1-sin²y = √1-x².Substituting this in (1),dy/dx = 1/√1-x² (or)d (arcsin x) / dx = 1/√1-x²Thus, the derivative of arcsin x (or) sin-1x (or) inverse sin x is 1/√1-...
What is the inverse of \begin{bmatrix} -4 & 15 & -8\\ -1 & 4 & -2\\ -1 & 8 & -1 \end{bmatrix}? Suppose that f has an inverse and f(-4)=2, f'(-4)= \frac{2}{5}. If g= \frac{1}{f^{-1, what is g'(2)? What equation is the inverse of y = 9x^...
Suppose f(x)=x^3+3x^2+x+4. Let g(x)=f^{-1}(x), the inverse of f(x). What is g'(4)? What is the inverse of the given relation y=7x^2-3. Given the following function f ( x ) = 3 x + 6 8 . Is there a Horizontal Shift? If so, state the direction. ...
Example 1: Find the derivative of y = cos −1 (x 3 ) for |x 3 | < 1 Solution: Note that |x 3 | < 1 if and only if |x| < 1, so the derivative is defined whenever |x| < 1. 4 d dx (cos −1 (x 3 )) = − 1 1 −(x 3 ) 2 d dx (x 3 ) = −...
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隐函数和反函数微分学(Implict Function and Inverse funtion differentiation)
Solve the system of linear equations by using inverse matrix formula. {x−2y=52x−3y=10 Solving System of Equations using Matrix Inverse: If we care given two or more than two equations, then we can write those equations in the form of the matrix given as X=A−1B , w...
Answer to: Find the inverse of AB if: A^-1 = -3 -5 -2 0 and B^-1 = -4 0 -1 3 By signing up, you'll get thousands of step-by-step solutions to your...
Inverse variation: y=k/x. Solve for x, providing each step: 27=3/x Show that Y is the inverse of X. Show that B is the inverse of A. Suppose f(x)=x^3+3x^2+x+4. Let g(x)=f^{-1}(x), the inverse of f(x). Wh...
State if the inverse of y = x^2 - 4 is a function. If f ( x ) and g ( x ) are inverse functions of each other, which of these equations does not always hold? a. g ( f ( x ) ) = x b. f ( g ( x ) ) = x c. f...