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The Derivative Calculator is an invaluable online tool designed to compute derivatives efficiently, aiding students, educators, and professionals alike. Here's how to utilize its capabilities: Begin by entering your mathematical function into the above input field, or scanning it with your camera.
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Dec 21, 2020 · Example \(\PageIndex{2}\):Using Properties of Logarithms in a Derivative. Find the derivative of \(f(x)=\ln (\frac{x^2\sin x}{2x+1})\). Solution. At first glance, taking this derivative appears rather complicated. However, by using the properties of logarithms prior to finding the derivative, we can make the problem much simpler.
Basic Idea. The derivative of a logarithmic function is the reciprocal of the argument. As always, the chain rule tells us to also multiply by the derivative of the argument.
Derivatives of logarithmic functions are mainly based on the chain rule.However, we can generalize it for any differentiable function with a logarithmic function. The differentiation of log is only under the base \(e,\) but we can differentiate under other bases, too.
The derivative is an important tool in calculus that represents an infinitesimal change in a function with respect to one of its variables. Given a function f x, there are many ways to denote the derivative of f with respect to x. The most common ways are. Start Fraction, Start numerator, d f , numerator End,Start denominator, d x , denominator ...
The derivative from above now follows from the chain rule. If [latex]y=b^x[/latex], then [latex]\ln y=x \ln b[/latex]. Using implicit differentiation, again keeping in mind that [latex]\ln b[/latex] is constant, it follows that [latex]\frac{1}{y}\frac{dy}{dx}=\text{ln}b.[/latex] Solving for [latex]\frac{dy}{dx}[/latex] and substituting [latex]y=b^x[/latex], we see that
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