Differentiate with respect to x. Find the logarithmic differentiation: y = \sqrt{\frac{(x + 3)(x - 2)}{2x - 1 Use logarithmic differentiation to find {y}' if x^{y} = y^{x}. Evaluate {y}'(1, 1) How to write the following function as an exponential function having a base ...
Solve: Differentiate \ the \ following: \int^{x^2}_{3x} \ sec^2 \ t \ dt. Differentiate the following function: f(x) = 5 \sin^2(x) - 8 \cos^2(x) Differentiate the function y=1- \cos^{2} x. Differentiate the function. A) f(x) = ln(5x cos^2 x) B) f(x) = 4^...
Thequotient rulecan be used to differentiatethe tangent functiontan(x), because of a basic identity, taken from trigonometry: tan(x) = sin(x) / cos(x). Step 1:Namethe top term f(x) and the bottom term g(x). Using our quotient trigonometric identity tan(x) = sinx(x) / cos(s),...
Topology.You may be surprised to learn that they do play a role indeed in physics! Algebraic equations. Approximation techniques. Series expansions: the Taylor series. Solving equations with complex numbers. Trigonometry: sin(2x)=2sinxcosx, etc. Infinitesimals. Differentiation. Differentiate basic ...
These formulas are quite useful if we are trying to integrate one of the six trigonometric functions, but if the trigonometric function is more involved or contains other functions, then we have to use a few other rules along with these formulas in order to integrate the function....
Differentiate the given functions by implicit differentiation: x^2-y+y^3=8, y^5+3x^2y^2+5x^4=12, cos(x-y)=ysinx. Find the derivative \frac{dy}{dx} by implicit differentiation if: 2x + ey = y^2 \cos(x + y) Find y'' be implicit differentiation. \sin y + \co...
Differentiate both sides of the double angle identity sin 2x = 2 sin x cos x to determine an identity for cos x. Find the first derivative. Write an expression for the following derivative. Consider the function f : [-1,1] \rightarrow \mathbb{R}\x \mapsto ...
How to differentiate sin^2(x) 1. y = In \ sin \ x - \frac{1}{2} sin^2x 2. y = x \ sinh (x^2) Prove that (sin(x) - sin(3x)) / (sin^2(x) - cos^2(x)) = 2sin(x) ? What does sin^2(x) - sinx simplify to?