Using the exponential definition of hyperbolic sin and hyperbolic cosine, prove: sinh (x + y) = sinh(x)cosh(y) + cosh(x)sinh(y). The hyperbolic cosine and sine function are defined by sinh(x) = (e^x-e^(-x))/2 and cosh(x) = (e^x+e^(-x))/2. Compute the derivatives and...
sinh2x=2sinhxcoshx Question: Prove the following identity: sinh2x=2sinhxcoshx Double Angle Sine Hyperbolic Function: To simplify the multiplication of hyperbolic functions using their exponential expressions given below, use the general algebraic formula and exponent rule of exp...
Prove that sinh(x-y) = sinh x cosh y - cosh x sinh y. 06:55 Prove that sinh(x+y)=sinhxcoshy+coshxsinhy 05:50 Prove that tanh(x-y)=(tanhx-tanhy)/(1-tanhxtanhy) 03:12 Prove that coth(x-y)=(cothx.cothy-1)/(cothy-cothx) 03:29 ("cosh x")/("1 -tanhx") + ("si...
Many functions, such as diff, int, taylor, and rewrite, can handle expressions containing sinh. Find the first and second derivatives of the hyperbolic sine function: syms x diff(sinh(x), x) diff(sinh(x), x, x) ans = cosh(x) ans = sinh(x) Find the indefinite integral of the hype...
this is a polynomial equation with respect to the unknown function v(ξ) and their derivatives v′(ξ),v″(ξ). We will obtain exact solutions to Eq. (70). Solutions to sinh-Gordon equation (66) may be calculated by using (69). Solutions to combined sinh–cosh-Gordon equation are ...
Find the derivative of the function and evaluate f'(x) at the given value of x. f(x) = \frac{4x + 5}{4x - 4}; x = 4 Calculate the derivative F'(x) of the function below; then find the value of the derivatives as specified. ...
// create the function value and derivatives double[] function = new double[1 + order]; function[0] = FastMath.sinh(operand[operandOffset]); if (order > 0) { function[1] = FastMath.cosh(operand[operandOffset]); for (int i = 2; i <= order; ++i) { function[i] = function[i ...
Prove that cosh^(2)x-sinh^(2)x=1 02:33 P.T cosh^(2)x+sinh^(2)x=cosh2x 03:03 Prove that cosh^(4)x-sinh^(4)x=cosh2x 03:56 Prove that cosh3x = 4 cosh^(3)x-3coshx 03:46 P.T tanh3x=(3tanhx+tanh^(3)x)/(1+3tanh^(2)x),AAx inR 06:07 Prove that (coshx+sinhx...
* @param resultOffset offset of the result in its array */ public void cosh(final double[] operand, final int operandOffset, final double[] result, final int resultOffset) { // create the function value and derivatives double[] function = new double[1 + order]; function[0] = FastMath...
Finding Derivatives of a Function | Overview & Calculations from Chapter 20 / Lesson 1 115K Understand what derivative calculus is and how to find the derivative of a function. Learn the derivative rules, and practice taking derivatives by following examples. Related...