Questions What Is The Derivative Of tan(x)? More Videos Derivative of \(tanx = sec^2x \) What Is The Derivative Of tan(x)? \( \frac{d}{dx} {tanx} = \frac{d}{dx} \frac{sinx}{cosx}\) [we know that \( tanx =\frac{sinx}{cosx} \)] \( => \frac{d}{dx} {tanx} = \frac{cosx \times \frac{d}{dx} {sinx} – \frac{d}{dx} {cosx} \times sinx}{cos^2x} \) [Use Quotient Rule] \( => \frac{d}{dx} {tanx} = \frac{cosx \times cosx – (-sinx) \times sinx}{cos^2x} \) [Simply] \( => \frac{d}{dx} {tanx} = \frac{cos^2x + sin^2x }{cos^2x} \) Use the Pythagorean identity for sine and cosine [\( sin^2x + cos^2x =1 \)] \( => \frac{d}{dx} {tanx} = \frac{1 }{cos^2x} \) we know that \( \frac{1}{cosx} =secx \) \( => \frac{d}{dx} {tanx} = sec^2x \) Related posts: What is Derivative of Sin(x)? What is The Formula of Cos(a+b)? Find all the Seventh roots of (3+4i) Which of the following numbers must be added to 5678 to give a reminder 35 when divided by 460? Related Topics: Up Next What Is The Greatest Common Factor Of 4k, 18k4, And 12? 2 4 2k 4k Don't Miss In simple interest what sum amounts of Rs.1120/-in 4 years and Rs.1200/-in 5 years ? Continue Reading Latest Popular Guest Post1 day ago 11 Cool Home Learning Space Ideas Guest Post1 day ago How To Manipulate And Create Directives In Angular? Guest Post2 days ago 11 Smart Ways Online Education is Blooming For Data Science Guest Post7 days ago What Is Alteryx And Its Purpose In Business Analytics? Guest Post1 week ago Power BI Tutorial – Introduction of Business Intelligence Guest Post1 week ago 5 Incredible Breakthroughs In The Realm Of Programming Languages Guest Post2 weeks ago How to Send Unlimited Bulk Emails using Python? Guest Post2 weeks ago What is Routing and How to use in Angular Application? LCM3 weeks ago Least Common Multiple (LCM) of 9 and 15 with Primes Guest Post3 weeks ago How Can I Learn SQL Programming Quickly? Math9 months ago Average Rate Of Change Formula Made Simple Math9 months ago List of Basic Maths Formulas for Class 5 to 12 Math2 years ago Percentage Formulas | How to Calculate Percentages of a Number? Math2 years ago Surface Area of a Triangular Prism Formula & Volume of a Triangular Math2 years ago Triangular Pyramid Formula | Volume & Surface Area of a Triangular Pyramid Math2 years ago Y Intercept & X Intercept Formula | Slope Intercept Form & Equation Math2 years ago What is (a-b)^3 Formula? a^3-b^3 Formula | (a-b)^2 | (a+b-c)^2 Math2 years ago What is Integration? List of Integration by Parts Formulas Math9 months ago List of Basic Algebra Formulas for Class 5 to 12 Math2 years ago What Is Loan Amortization Formula? Calculation & Example? Advertisement