Differentiate the function: {eq}y = x + \frac{2}{x} + \frac{2}{x^2} {/eq} Derivative: The derivative of the sum (or difference) of two or more functions is the sum (or difference) of derivatives of the function
Answer and Explanation: Learn more about this topic: Function Differentiation Using Chain Rule | Formula & Examples from Chapter 8/ Lesson 6 54K Learn how to differentiate a function using the chain rule of differentiation. Find various chain rule derivative examples with various function types. ...
% Since we know the formula and when it starts and stops each piece % we can compute the derivative analytically: dLdt = zeros(1,length(L)); range1 = t>=0 & t<=20; dLdt(range1) = -0.5; range2 = t>40 & t<=60; dLdt(range2) = 0.5; ...
1. Identify the Function: We have y=tanx. Recall that the tangent function can be expressed in terms of sine and cosine: tanx=sinxcosx 2. Apply the Quotient Rule: Since tanx is a quotient of two functions (sine and cosine), we will use the quotient rule for differentiation. The quo...
COUNTIF Function The formula or syntax for the COUNTIF function is as follows: =COUNTIF(range, criteria) You will require the following arguments to perform a task with this function: ArgumentRequired/OptionalExplanation range Required Indicates the range of cells where the function will apply the...
The derivative of the expression of the given type is solved easily with the following two formulas: One is the power rule that is given by: {eq}\frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1} {/eq} another is the formula of differentiation of exponential function: {eq}\frac{d}{...
Answer and Explanation:1 Givenf(x)=sin(sinx) Differentiating, we get ddxf(x)=ddxsin(sinx) ... Learn more about this topic: Function Differentiation Using Chain Rule | Formula & Examples from Chapter 8/ Lesson 6 54K ...
This pattern suggests the following general formula for powers of n where n is a positive integer. Power Rule In fact, the power rule is valid for any real number n and thus can be used to differentiate a variety of non-polynomial functions. The following example illustrates some applications...
The function differentiates each polynomial piece separately, and ignores jump discontinuities between polynomial pieces during differentiation. For the B-form, the function uses the [PGS; (X.10)] formulas for differentiation. For the stform, differentiation relies on knowing a formula for the ...
Using the formula for differentiation of one function with respect to another:ddx(fg)=f′g−fg′g2However, since we are looking for f′(x)g′(x), we can simplify:f′(x)g′(x)=f′(x)g′(x) Step 5: Final CalculationAfter calculating f′(x) and g′(x), we can simplify:f...