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 Math5 days ago List of all Basic Limit Formulas Math5 days ago List of all Basic Profit and loss Formulas Math5 days ago List of all Basic Perimeter & Area formulas of Quadrilateral Guest Post1 week ago How to Prepare for Salesforce Certification? Math2 weeks ago List of all Basic Area & Surface area Formulas Math2 weeks ago List of all Basic Semicircle Formulas Math2 weeks ago Proof of Pythagoras Theorem & Formulas Math2 weeks ago List of all Basic Perimeter Formulas Questions3 weeks ago one number is 2 more than 3 times another. their sum is 22. find the numbers Questions3 weeks ago a line passes through the points (0,3) and (2,-9). what is the equation of this line in alope-intercept form Math6 months ago Average Rate Of Change Formula Made Simple 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 Percentage Formulas | How to Calculate Percentages of a Number? Math6 months ago List of Basic Maths Formulas for Class 5 to 12 Math2 years ago List of Pyramid Formula – Surface Area, Volume of Pyramid Math2 years ago What is Integration? List of Integration by Parts Formulas Math6 months ago List of Basic Algebra Formulas for Class 5 to 12 Math1 year ago What Is Loan Amortization Formula? Calculation & Example? Math2 years ago Y Intercept & X Intercept Formula | Slope Intercept Form & Equation Advertisement