Derivative of sec^2 x by first principle method
Finding the Derivative of sec^2(x) : Mathematically, The derivative of sec square x is equal d(sec^2x)/dx = 2 sec2x tanx or if we express it in words then derivative of sec 2 x formula is equal to 2 multiply by (sec2x)(tanx). We can drive the formula of the derivative of sec^2x by using following methods of differentiation –
- The chain rule method
- Product rule
- Quotient rule of derivatives
- The first principle of derivatives, that is, the definition of limits.
What is Derivative of Sec^2x?
The derivative of sec 2 x is equal to 2(sec2x)(tanx). Mathematically in terms of derivative form it can be written as d(sec2 x)/dx = 2sec2x tanx. As we all know that Sec x is very important trigonometric functions. To derive the derivative of sec2x we need the formula of derivative of sec x. Now we must know the derivative of sec X, which is equal to (secx)(tanx). After that by using the power rule of differentiation we can find the derivative of sec square x.
For the next step we must we know the power rule of differentiation –
- d(xn)/dx = n x(n-1), Using this formula, we can write the formula for the differentiation of sec square x
- d(sec2x)/dx = 2 (sec x) × d(secx)/dx
- d(sec2x)/dx = 2 (secx) (secx * tanx)
- = 2 sec2x tanx.
- So we can read it as d(sec2x)/dx = 2 sec2x tanx
Derivative of Sec2 x using Chain Rule
If you want to find the derivatives of composite functions then you have to use The chain rule of derivatives.
- As we know that Sec2 x is the composite function of two functions f(x) = x2 and g(x) = secx given by, h(x) = f o g (x) = sec^2x. Now, to find the derivative of sec 2 x, we use the formula of chain rule given by, h'(x) = [f(g(x))]’ = f'(g(x)) × g'(x). Hence, using this formula, the power rule of derivatives and the derivative of secx, we have
- d(sec2 x)/dx = 2 sec2-1x × d(secx)/dx
- = 2 (secx) × (secx * tanx)
- = 2 (sec2x)(tanx)
- Hence, the derivative of sec square x is equal to 2 (sec2x)(tanx).
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