The derivative of logarthmic functions: If y = ln x, then y' = 1/x and if y = logaa x, then y' = 1/[(log a) x]The derivative of an exponential function: If y = a x , y = ax log aDifferentiation of Trigonometric FunctionsHere are the derivatives of trigonometric functions....
In Maths, differentiation can be defined as a derivative of a function with respect to the independent variable. Learn its definition, formulas, product rule, chain rule and examples at BYJU'S.
c. $ 6x^4+\tan y=3y^2-4x$ 3. Given the implicit equation, $4x^2-9y^2 = 36$, use implicit differentiation to determine the following: a. Expression for $y’$. b. Slopes of the tangent lines passing through the equation’s curve and the points, $\left(-5, \dfrac{8}{3}\rig...
the derivative is the ratio of the infinitesimal change of the output over the infinitesimal change of the input producing that change of output. Geometrically, for a real valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the ...
2. Take the derivative of y = 2x2 / (x - 1) 3. Take the derivative of y = (x - 1)(x2) 4. Take the derivative of y = ex 5. Take the derivative of y = ln(x) Solutions 1. Derivative of trigonometric function and chain rule. y' = -sin(2x)(2) y' = -2sin...
Use logarithmic differentiation to find the derivative of the function. y = x^{ln(x)}. Use logarithmic differentiation to find the derivative of the function: y = (\cos 3x)^x Use logarithmic differentiation to find the derivative of the function. y ...
Use implicit differentiation to find dy/dx: y^2 - 2xy = 0. Use implicit differentiation to find dy/dx: x^3 y^2 - y^3 = 3x - 9 . 1. Use implicit differentiation to find \frac{dy}{dx} . 2x^{4}+3y^{3}=5xy Use implicit differentiation to find dy/dx. 4x^{...
functions. Showthe intermediate steps and refer to the rules D1-D5 on page 14 of the lecturenotes when using them. Be careful with the product and quotient rules as well asthe chain rule.(a) f(x)=5xex+sin(x)(b) f(x)=x33+xln(...
All derivative formulas and techniques are to be used in the process of implicit differentiation as well. ☛Related Topics: Derivative Calculator Calculus Calculator Second Derivative Calculator Differentiation Implicit Differentiation Examples Example 1:Find dy/dx by implicit differentiation: 3x + 2y = ...
If we have some function of f(x) = xn where n is a integer. dxndx = n xn-1 Example Differentiate, x3, 4x3, 4x2-6x + 6 Answers: 3x2, 12x2, 8x - 6 Chain Rule Given f(x) which is a function of another function g(x). Then h(x)=f(g(x)). The derivative is given by...