In summary, to differentiate y=e^x, we use the rule for differentiating the inverse of a function since the exponential function is the inverse of the natural logarithmic function. This gives us the derivative of e^x as e^x. For y=lnx, we can use implicit differentiation with the help ...
Differentiate the equation. This question is an example of the chain rule in calculus, where one function is located within another function; in mathematical notation, this is written as f(g(x)), where g(x) is a function within the function f. The chain rule is written as y' = f'(g...
For the function f(x,y) where x and y are functions of variable t, we first differentiate the function partially with respect to one variable and then that variable is differentiated with respect to t. The chain rule is written as: Example Let’s take a look at an example that shows...
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AP Calculus AB Skills Practice Jump to a specific example Andrew Noble View bio Steps for How to Differentiate Vertical Asymptotes from Discontinuities Step 1:Factor the numerator and denominator if necessary. Step 2:For the denominator, identify the values of {eq}x {/eq} that make {eq}f(...
How to Differentiate tan(x) 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...
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Calculate this using differential calculus. Marginal revenue is the derivative of the product's revenue with respect to its quantity. Obtain or estimate a relationship between the item's price and the quantity of units that you sell. This function forms the item's demand curve on a graph. ...
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Differentiating with respect to a function requires Calculus of Variations. People often propose that you substitute a variable for the function and differentiate with respect to that. However a number of years ago I posted an example of a case where that would produce the wrong answer. ...