Change the base to ee f(x)=2x=(eln2)x=e(ln2)xf(x)=2x=(eln2)x=e(ln2)x Step 2 Differentiate, recalling that ddx(ekx)=kekx)ddx(ekx)=kekx). In this case, k=ln2k=ln2. f′(x)=ln2e(ln2)xf′(x)=ln2e(ln2)x Step 3 Convert the base back to...
Differentiate a constant function. The derivative of a constant is zero. For example, if f(x) = 5, then f'(x) = 0. Step 2 Apply the power rule to differentiate a function. The power rule states that if f(x) = x^n or x raised to the power n, then f'(x) = nx^(n – 1...
Exponential Function The exponential function has the form {eq}y=ab^{x} {/eq}, where {eq}b {/eq} is the base which must be greater than zero and other than {eq}1 {/eq}. {eq}x {/eq} is the independent variable. To obtain the graph of an exponential function, we substitute val...
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...
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 ...
How to differentiate of exponential and Logarithmic functions Solve the following logarithmic equation for the value of x: log_9(x-5) + log_9(x+3) = 1. Convert to a logarithmic equation: 27^x=81 Explore our homework questions and answers library ...
we need to be familiar with some of its basic components. Without loss of generality, we are going to define the exponential function as {eq}y = a^{x} {/eq}. Hence, we can also define an exponential expression taking the form of {eq}a^{x} {/eq}. We will be using such forms ...
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How to Find Maximum and Minimum When graphing a quadratic function, there are a few attributes that we can use to differentiate them. One of these is the vertex, which is the point where a parabola is at its minimum or maximum value and continues upward or downward from there. There are...
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