Example 1: What is the derivative of ln(2x)? Notice that the chain rule can be used here to find the derivative. In this case, the inside function is 2x, and the outside function is ln(x). Therefore, ddxln(2x)=12x⋅ddx2x=12x⋅2=1x. It is an interesting result that ...
The input recognizes various synonyms for functions such asasin,arsin,arcsin,sin^-1 Multiplication signs and parentheses are automatically added — for example2sinxbecomes2*sin(x) List of supported functions and constants: •ln(x)—natural logarithm ...
Derivatives of functions tableFunction nameFunctionDerivative f (x)f '(x) Constant const 0 Linear x 1 Power x a a x a-1 Exponential e x e x Exponential a x a x ln a Natural logarithm ln(x) Logarithm logb(x) Sine sin x cos x Cosine cos x -sin x Tangent tan x Arcsine arcsin...
d/dx arcsin(x) = 1/sqrt(1-x2) d/dx arccos(x) = -1/sqrt(1-x2) d/dx arctan(x) = 1/(1+x2) Applications of the Derivative The derivative comes up in a lot of mathematical problems. An example is finding the tangent line to a function in a specific point. To get the slope...
The common derivative helps us to differentiate the common functions, such as the logarithmic function, exponential function, and so on. For example, the derivative of the natural logarithm of x is equivalent to the inverse of x. Mathematically, this can be stated as, ...
Sine function: for example, 30 degree sine: sin30 Cosine function: for example: cosine of 60 degrees: cos60 Tangent function: for example: 45 degree tangent: tan45 Arcsine function: for example: arcsin0.5 or asin0.5 Arccosine function: for example, arccosine of 0.5: arccos0.5 or acos0.5...
Derivative of a Composite Function A composite function is a function whose input is another function. For example, f(g(x)) and h(T(z)) are composite functions. Finding the derivative of a composite function requires the chain rule. The chain rule says that for two functions, f(g(x))...
The well-known derivative ln(x) is one that students often find easy to memorize due to many real-life applications. Learn the step-by-step process used to solve the derivative and the application of the derivative of ln(x) using a real-world example. ...
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Firstly, we removed the arcsine and square-root arithmetic operations (Step 3 of Algorithm 4.2) and replaced them with the comparator method. This reduces the resources needed for that step. Secondly, we replaced the piecewise polynomial implementation of the exponential function...