How do you find the derivative of \displaystyle{y}={\sec{{4}}}{x} ? What is derivative of sec x? The derivative of sec x with respect to x is sec x · tan x.

Understanding the Context

I. e. , it is the product of sec x and tan x. We denote the derivative of sec x with respect to x with d/dx (sec x).

Differentiate: x^3sec x | Maths Questions

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Differentiate: x^3sec x | Maths Questions
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Key Insights

The derivatives of \sec (x), \cot (x), and \csc (x) can be calculated by using the quotient rule of differentiation together with the identities \sec (x)=\frac {1} {\cos (x)}, \cot (x)=\frac {\cos (x)}. The derivative calculator supports solving first, second. , fourth derivatives, as well as implicit differentiation and finding the zeros/roots. You can also get a better visual and understanding. Khanmigo is now free for all us educators!

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Final Thoughts

Plan lessons, develop exit tickets, and so much more with our ai teaching assistant. The secant of an angle designated by a variable x is notated as sec (x). The derivative rule for sec (x) is given as: D⁄dxsec (x) = tan (x)sec (x) this derivative rule gives us the ability to quickly. Differentiate using the chain rule, which states that d dx [f (g(x))] d d x [ f ( g ( x))] is f '(g(x))g'(x) f ′ ( g ( x)) g ′ ( x) where f (x) = sec(x) f ( x) = sec ( x) and g(x) = 4x g ( x) = 4 x. The derivative of with respect to is. The derivative of $\boldsymbol{\sec x}$ returns the product of $\boldsymbol{\sec x}$ and $\boldsymbol{\tan x}$.

We can prove this derivative by differentiating. Differentiate using the chain rule. Given f (x) = g(h(x)) then. F '(x) = g'(h(x)) × h'(x) ← chain rule.