Differentiation means the rate of change of one quantity with respect to another. Learn to find the derivatives, differentiation formulas and understand the properties and apply the derivatives.
Formulas used: 1.Chain Rule of Differentiation: {eq}\displaystyle f(g(x))'=f'(g(x))g'(x) {/eq}. 2.Product Rule of Differentiation: {eq}\displaystyle (uv)'=uv'+vu' {/eq}. 3.{eq}\displaystyle (x^n)'=nx^{n-1} {/eq}. ...
First Principle of Differentiation:A derivative is the first of the two main tools of calculus (the second being the integral). It is theinstantaneous rate of change of a function at a point in its domain. This is the same thing as the slope of the tangent line to the graph of the fu...
Now that we know the value of log e to be equal to 0.4342944819, we will try finding this value using different formulas and properties of the exponential and logarithmic functions. Using the change of base in log function formula, we can write log e OR log10e as logee/loge10. So, we...
In this paper, we present the fractional backward differentiation formulas for the numerical solutions of two-term fractional differential Sylvester matrix equations in the Caputo derivative sense, which includes the celebrated two-term fractional differential Lyapunov matrix equations. ...
If we have a function {eq}F(x,y,z) {/eq}, we can compute {eq}\dfrac{\partial z}{\partial x} {/eq} and {eq}\dfrac{\partial z}{\partial y} {/eq} using implicit derivation by using the following formulas: {eq}\dfrac{\partial z}{\pa...
We develop formulas for derivatives of this type of function in stages, beginning with positive integer powers. Before stating and proving the general rule for derivatives of functions of this form, we take a look at a specific case, ddx(x3)ddx(x3). Differentiating x3x3 Find ddx(x3)ddx(x3...
Explicit differentiation is used when 'y' is isolated, whereas implicit differentiation can be used similar to the chain rule when 'y' is not isolated. Learn more about implicit differentiation through examples of formulas and graphs. Related to this Question ...
of mathematical functions. Some differentiation rules describe the predictable patterns seen in the derivatives of various types of basic functions, such as powers and exponentials, while other more general rules can be applied to differentiate complicated formulas which combine multiple types of ...
In other word, the main target applications presented in Section 4, motivate us to develop differentiation formulas with respect to parameters, which is really the important subject of the paper. For details one can refer to Section 4. Numerical examples for computing integrals presented in recent...