Derivative of Tan | Differentiation & Formula - Lesson - Study.com
2023年11月21日 · The differentiation of tan(x) is a vital step towards solving math and physics problems. To review this differentiation, the derivative of tan(x) can be written as:
How do you find the derivative of #y=tan(x)# using first ... - Socratic
2018年7月6日 · See all questions in Derivative Rules for y=cos(x) and y=tan(x) Impact of this question. 64577 views ...
What is the derivative of #y=tan(x)# - Socratic
2014年8月18日 · The derivative of tanx is sec^2x. To see why, you'll need to know a few results. First, you need to know that the derivative of sinx is cosx. Here's a proof of that result from first principles: Once you know this, it also implies that the derivative of cosx is -sinx (which you'll also need later). You need to know one more thing, which is the Quotient Rule for differentiation: …
How do you take the derivative of #Tan^-1 (y/x)#? - Socratic
2015年6月7日 · I'm assuming you are thinking of this as being a function of two independent variables x and y: z=tan^{-1}(y/x).
How do you find the derivative of - Socratic
2016年11月4日 · dy/dx = sec^2x By definition If y=f(x) then: dy/dx=f'(x) =lim_(hrarr0)( (f(x+h)-f(x))/h ) So, with y=tanx we have: dy/dx = lim_(h rarr0)((tan(x+h)-tanx)/h) Using the ...
What is the antiderivative of #tan(x)#? - Socratic
2014年10月16日 · Recall: int{g'(x)}/{g(x)}dx=ln|g(x)|+C (You can verify this by substitution u=g(x).) Now, let us look at the posted antiderivative. By the trig identity tan x={sin x}/{cos x}, int tan x dx=int{sin x}/{cos x}dx by rewriting it a bit further to fit the form above, =-int{-sin x}/{cos x}dx by the formula above, =-ln|cos x|+C or by rln x=lnx^r, =ln|cos x|^{-1}+C=ln|sec x|+C I hope that this …
What is the derivative of #y=tan(x) sec(x)#? - Socratic
2014年8月29日 · The derivative of #y = tan(x)sec(x)# with respect to #x# is #(dy)/(dx) = sec^3(x) + sec(x)tan^2(x)#. To perform this differentiation, we will need to use the Product rule, which states that given the product of two functions, #u(x)v(x)#, here represented as #f(x) = u(x)v(x)#...
How do you find the derivative of x^tanx? - Socratic
2015年8月4日 · Use logarithmic differentiation: let #y=x^{tan(x)}# so that #ln(y)=ln(x^{tan(x)})=tan(x)ln(x)#. Now differentiate both sides with respect to #x#, keeping in mind that #y# is a function of #x# and using the Chain Rule and Product Rule: #1/y * dy/dx=sec^{2}(x)ln(x)+tan(x)/x# Hence, #dy/dx=y * (ln(x)sec^{2}(x)+tan(x)/x)#
What is the derivative of #y=e^(tan(x))#? - Socratic
2018年6月18日 · e^tan(x)/cos^2(x) This is a composite function, i.e. a function composed by two functions f(x) and g(x). The output of the inner function is used as input for the outer function, in the form f(g(x)). In this case, the outer function is the exponential e^x, while the inner function is the tangen function tan(x). The differentiation of a composite function is governed by the chain …
What is the derivative of tan^2 x? - Socratic
2017年10月11日 · Calculus Differentiating Trigonometric Functions Derivative Rules for y=cos(x) and y=tan(x) 1 Answer