2014年8月30日 · The derivative of y=arctan x is y'=1/{1+x^2}. We can derive this by using implicit differentiation. Since ...

The derivatives of inverse trigonometric functions can be computed by using implicit differentiation followed by substitution.

2014年7月31日 · Using implicit differentiation, taking care to use the chain rule on tan y, we arrive at: 3.) sec^2 y dy/dx = 1 Solving for dy/dx gives us: 4.) dy/dx = 1/(sec^2 y) Which further simplifies to: 5.) dy/dx = cos^2 y Next, a substitution using our initial equation will give us: 6.) dy/dx = cos^2(arctan x) This might not look too helpful, but there ...

2016年6月6日 · Note that #cos^2(arctan(x^2))# can be simplified. If #arctan(x^2)# is an angle in a right triangle, then #x^2# is the side opposite the angle and #1# is the side adjacent to the angle. Then, by the Pythagorean Theorem, #sqrt(1+x^4)# is the triangle's hypotenuse.

2016年7月30日 · 2/(4+x^2) >differentiate using the color(blue)"chain rule" color(red)(|bar(ul(color(white)(a/a)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(a/a)|))).....

2017年2月8日 · y' = 1/(1 + sin^2 x) cos x It is the derivative of a function arctan, of a function sin. It is equal to the derivative of the first function arctan, expressed in terms of its argument, multiplied by the derivative of the argument with respect to x. The derivative of arctan u is 1/(1 + u^2). When u is sin(x) it is simply 1/(1 + sin^2 x). The …

2014年9月5日 · This is a case of knowing the how the derivative of inverse tangent works, and then following the chain rule. If we were looking at y=arctan(x), there's a way to determine the derivative if you've forgotten the formula. First remember that arctan(x) means "inverse tangent of x," sometimes written as tan^(-1)(x). To invert means to switch the x and the y (among other things, but that's the ...

2016年8月6日 · 30219 views around the world You can reuse this answer ...

2014年10月5日 · Recall: (arctanx)'=1/{1+x^2} By Chain Rule, y'=1/{1+(3x)^2}cdot(3x)'=3/{1+9x^2} I hope that this was helpful.

2016年9月23日 · Note that this matches the other answer, as using the triangle, we can also see that #cos(arctan(x)) = 1/sqrt(x^2+1)#