CBSE Class 11-science Answered

Differentiation of a function gives the rate of change or slope the function graph at a particular point.

If we plot a function f(x) = 2x³ as we change x values, we can plot on it tangents to the curve at any point.

What's the slope of that particular tangent? It's given by the derivatitve of the function.

How to obtain the derivative of a given function?

To obtain derivative, we have to split the function into elementary function such as only xⁿ term or sin x or cosx and so on.

For example f(x) = x⁴ + sinx + cosx, is a function which is obtained by addition of three elementary function x³, sinx and cosx.

To obtain the drivative of this function we have to take derivative of elementary function and add.

df(x)/dx = 4x³ + cosx - sinx,

Similarly we do if elementary function are subtracted, but for product and quotient, there are product and quotient rules, which can be easily found in the text book.

Some derivative of common elementary functions are,

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