How do you find the equation of a normal line to a curve at a given point? How do I find the integral #int (x*cos (5x))dx# ? How do you find the derivative of #y=x^tan (x)#? How do you …

The function f (x) = secx + cosx is convex at x=pi/3 To determine whether a function is concave or convex at a given point, recall that we find the second derivative of that function, and insert our …

I assume that the poster meant: y=e^x tan sqrt {5x} By rewriting the square-root as the 1/2-power, y=e^xtan (5x)^ {1/2} Let us now find the derivative.

(0, 0) From Wikipedia: a critical point or stationary point of a differentiable function of a single real variable, f(x), is a value x_0 in the domain of f where its derivative is 0: f′(x_0) = 0 Thus, to find …

What is the antiderivative of #sqrt (x+3)#? How do you factor the expression # 81x^ (4/5) - 256#? Integrals of (sec^ (2) (x))/ (tan (x))? How do you prove # (1+tan^2x)/ (1-tan^2x)=1+tan2x.tanx# …

Recall that (tan^ {-1}x)'=1/ {1+x^2} Let us find the derivative of F (x)=tan^ {-1} (x/sqrt {1+x^2}). (I hope that this is the function you had in mind.) By Chain Rule, F' (x)=1/ {1+ (x/sqrt …

Questions and Videos on Differentiating Inverse Trigonometric Functions, within Calculus

(df)/ (dx)= (8x^3)/ (x^8-2x^4+2) and tangent at (1,0) is y=8x-8 Derivative of tan^ (-1)x is 1/ (1+x^2) Now we have f (x)=2tan^ (-1) (x^4-1) Hence f' (x)= (df)/ (dx)=2 ...

Take the negative at the front and cancel with the negative inside the second sin function and multiply the top and the bottom by #1/2# to take the factor of #2# at the top and place on the …

Drawing a right triangle with an angle y such that tan(y) = x − 1, we can find that sec(y) = √x2 − 2x + 2. Plugging that in, we get our result: d dx arctan(x − 1) = 1 x2 − 2x +2 Note that the same …