2016年6月5日 · To find the derivative of secant, we could either use the limit definition of the derivative (which would take a very long time) or the definition of secant itself: #secx=1/cosx# We know #d/dxcosx=-sinx# - keep that in mind because we're going to need it. Our problem is: #d/dxsecx# Since #secx=1/cosx#, we can write this as: #d/dx1/cosx#

2014年12月11日 · Let y=sec^{-1}x. by rewriting in terms of secant, => sec y=x by differentiating with respect to x, => sec y tan y cdot y'=1 by dividing by sec y tan y, => y' = 1/{sec y tan y} since sec y =x and tan x = sqrt{sec^2 y -1}=sqrt{x^2-1} => y'=1/{x sqrt{x^2-1}} Hence, d/dx(sec^{-1}x)=1/{x sqrt{x^2-1}} I hope that this was helpful.

2015年8月31日 · Calculus Differentiating Trigonometric Functions Derivative Rules for y=cos(x) and y=tan(x) 1 Answer

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 ...

2014年12月18日 · Answer d/dx sec(x^2)= sec(x^2)tan(x^2)2x Explanation To solve this question, you would need to use the chain rule (and later on, the quotient rule as well). In sec (x^2), you can quite easily identitfy the "inner" and "outer" functions present to use the chain rule. The "inner" function is x^2, because it is composed/inside of in the sec. The chain rule is: …

2015年6月22日 · To find the antiderivative (or integral), there is a trick to this. #intsecxdx# You can multiply by #(secx + tanx)/(secx + tanx)#.

2014年12月17日 · What is the derivative of #sec^2(x)#? Calculus Differentiating Trigonometric Functions Derivatives of y ...

2014年8月6日 · sec x is equal to 1/cosx. Thus, sec^3 x is an equivalent statement to 1/(cosx)^3. And, we know that this is equivalent to (cos x)^(-3). So, all we need to do is use the power rule, keeping in mind to use the chain rule on cos x: dy/dx = -3*(cos x)^(-4) * d/dx[cos x] = -3*(cos x)^(-4) * (-sinx) = 3sinx(cos x)^(-4) = (3sinx)/(cos^4 x)

2023年11月21日 · Well, again using our derivative rules for trig functions and linear properties of derivatives, I know that the derivative of f(x) = (1/2)sec^2(x) - cos(x). If I graph this, I see below that the ...

Finding the derivative of sec^2(x) involves the use of two derivative formulas plus the chain rule. Discover the steps used to solve the derivative of sec^2(x) and how to check one's work using ...