[{"_1":2,"_45":-5,"_46":-5},"loaderData",{"_3":4,"_20":-5,"_21":22},"root",{"_5":6,"_7":8,"_9":10,"_11":12,"_13":14,"_15":16,"_17":18,"_19":-5},"theme","yts","flashMessages",{},"env","production","broadcasts",[],"cookies","cmptl2jmi50ut2zbebwbth1g=e%3AS20uYkjHCAXhk3_BC8gUPENEKpFN4eCQssNpVpagNI5Du7SufIqY2FyRRTlgjfwMMjhFKr-ucoPXREtWQ_POr1cxNQzPnlv4Sl1FJl4wC5wgXezJGaA0bdRjFKHgAT4K.dWdWdzBxTFdKLWxLS2o2OA.48S6FcrXtU4j1V2u-ottH70ukxL3fHrZN0kqJMQRoIg; adonis-session=s%3AeyJtZXNzYWdlIjoiY21wdGwyam1pNTB1dDJ6YmVid2J0aDFnIiwicHVycG9zZSI6ImFkb25pcy1zZXNzaW9uIn0.wSJZ3u5zrvIz7fbUPmiS0m_dWD0zNZosNNp60inLseM","isSandbox",false,"token","live_426b3df591363e8b8f48cb36ce5","user","routes/_auth+/_layout","routes/_auth+/r.$revisionId+/_index",{"_23":24,"_31":32,"_39":40,"_41":16,"_42":16,"_43":44},"response",{"_25":26,"_27":28,"_29":30},"resultType","static","language","en","html","

Numerical differentiation - simply explained

Calculating Derivatives Numerically

\n
To calculate the slope of a line, first select two arbitrary points and find their coordinates.
\n
\n
The slope of a line can be derived from the difference between the Y-values of the two points.
\n
\n
The slope calculation involves determining the change in Y divided by the change in X.
\n
\n
This method enables the computation of derivatives numerically.
\n
\n
\"This is the equation of the line which has the slope of 2.\"
\n

\n
\"Remember that the slope of a straight line can be calculated by selecting two arbitrary points and determining the difference in Y-values.\"
\n

Understanding Derivatives and Slopes

\n
Derivatives represent the rate of change or slope of a function at a specific point.
\n
\n
By using numerical methods, such as selecting points close to each other, we can approximate derivatives effectively.
\n
\n
If H decreases towards zero, the derivative estimate becomes more accurate.
\n

\n
\"By decreasing the value of H, we can approach the true derivative value of the function at a specific point more accurately.\"
\n

Enhancing Derivative Calculation

\n
A more precise estimation of derivatives can be achieved by selecting points on both sides of the desired point.
\n
\n
This method provides a better approximation compared to a single-point calculation.
\n
\n
Dividing by 2H when using points on both sides generally yields improved results.
\n

\n
\"Selecting points on both sides of the desired point can enhance the accuracy of derivative calculations.\"
\n

Calculating Second Derivatives Numerically

\n
Second derivatives indicate the rate of change of the slope of a function.
\n
\n
The process of calculating second derivatives numerically involves adjusting the calculation formula slightly to account for the second derivative.
\n

\n
\"Calculating second derivatives numerically requires a modification in the calculation formula to account for the second derivative.\"
\n

Simplified Numerical Differentiation Process

\n
Setting X to 1 and applying the equation allows for the calculation of the derivative at that specific value.
\n
\n
By setting a small value for H, a straightforward function to compute the numerical derivative is created.
\n
\n
The function is then utilized to find the derivative for a given X value.
\n

\n
Calculating the derivative at a specific point simplifies the differentiation process by using numerical values rather than complex mathematical manipulations.
\n

","videoInfo",{"_33":34,"_35":36,"_37":38},"videoId","pitoyz9Il9c","videoTitle","Numerical differentiation - simply explained","videoAuthor","TileStats","revisionId","ULI2dea0BNXdeqSHLuxWw","showTimestamps","loggedIn","questions",[],"actionData","errors"]