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 ...
Example 1 ff x 2 1 Solution to Example 1 Method 1 ff ff xx x=2y+2x=2y+2 xx yy ff Method 2 f′f′ 1212 df−1dx=1f′(f−1(x))df−1dx=1f′(f−1(x)) 1 2 Note Example 2 dydxdydx y=arcsinxy=arcsinx Solution to Example 2 ...
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. ...
What is the derivative of x \ sin(\frac {1}{x}) What is the derivative of 3 \ cot(n)(\theta) What is the derivative of the function y = 5t^6 - 12 sqrt(t + (4/t)) ? What is the derivative of the function y = arcsin(x^2)? What is the derivative of this function? y...
Taking the Derivative of arcsin: How-To & Tutorial Proving the Sum & Difference Rules for Derivatives Using the Derivatives of Natural Base e & Logarithms Calculating Derivatives of Constant Functions P-Series Test | Definition, Convergence & Examples ...
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...
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...
Example: Find the derivative of: 3x2+ 4x. According to the sum rule: a= 3,b= 4 f(x) =x2,g(x) =x f '(x) = 2x,g'(x) = 1 (3x2+ 4x)' = 3⋅2x+4⋅1 = 6x+ 4 Derivative product rule (f(x) ∙g(x) ) ' =f '(x) g(x) +f(x)g'(x) ...
The inverse of sin function or sin-1, also known as arcsin or asine obtains the angle ϴ if it takes the ratio \[\frac{\text{Opposite side}}{\text{Hypotenuse side}}\] Sine Inverse is represented by sin-1or arcsin. Sin Inverse Example ...
Find the derivative of the function f(x) = \arcsin x + x \sqrt {1 - x^2}. Find the derivative of the function f(x) = sqrt 4x^3. Find the derivative of f(x) = \frac{\ln(x)}{5 \sqrt x + 2}. Find the derivative of ...