Derivative f’ of the function f(x)=tan x is: f’(x) = 1 + tan²x for any value x different of π/2 + kπ avec k ∈Z Derivative of tan x Derivative $f’$ of the function $f(x)=\tan x$ is: \(\forall x \neq \frac{\pi}{2}+k\pi, k \in \mathbb{Z}, f'(x)...
Derivative of tangent function$g(x)=\tan x$ is: \(\forall x \neq \dfrac{\pi}{2}+k\pi, k \in \mathbb{Z}, \quad g'(x) = 1+\tan ^{2} x\) So, we have: \[\begin{aligned} f^{\prime}(x)&=\frac{1}{\tan^{\prime}(f(x))}\\ &=\frac{1}{1+\tan^2(f(x))}\...
Prove the derivative of tan x.Question:Prove the derivative of tan x.Derivatives:The derivative of a function can be found using the formal definition of the derivative. Suppose f(x) is continuous at a point c, then f(x) is said to be differentiable at c ...
Find the derivative of f(tan x) w.r.t. g (sec x) at x=π4, where f'(1)=2 and g'(√2)=4. A 1√2 B √2 C 1 D 0 Video Solution Struggling with Differentiation ? Get free crash course Text SolutionVerified by Experts The correct Answer is:A Let u=f(tanx) and v=g(...
Note: the little mark ’ means derivative of, and f and g are functions.Common FunctionsFunction Derivative Constant c 0 Line x 1 ax a Square x2 2x Square Root √x (½)x-½ Exponential ex ex ax ln(a) ax Logarithms ln(x) 1/x loga(x) 1 / (x ln(a)) Trigonometry (x is...
i)(cosx)′=−sinxii)(tanx)′=sec2xiii)(tanu)′=sec2uu′ with u a function of xAnswer and Explanation: We have a function composed of the tangent function whose argument is the trigonometric function cosine. We must apply the rule for the derivative of......
{eq}y=\sec x (\tan x - \sec x) {/eq} The derivative of {eq}y {/eq} with respect to... Learn more about this topic: Finding Derivatives of a Function | Overview & Calculations from Chapter 20/ Lesson 1 117K Understand what derivative calculus is and how to find the derivative ...
Find the derivative of tan(2x+5) with respect to x by using first principle of derivative. View Solution Knowledge Check Find the derivative of xsinx with respect to x. A(xcosx−sinx) B(3xcosx+sinx) C(xcosx+sinx) D(cosx+sinx)SubmitFind...
Learn how to differentiate and find the derivative of cot(x). See the proof of the derivative of the cotangent function and find explanations for...
The derivative of tan xd dx tan x = sec2x Now, tan x = sin x cos x . (Topic 20 of Trigonometry.)Therefore according to the quotient rule:d dx tan x = d dx sin x cos x = cos x· cos x − sin x(−sin x) cos2x = cos2x + sin2x cos2x = 1 cos2x = sec2x....