The derivative of cos(x) with respect to x is - sin(x). Combine terms. Tap for more steps... Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.

The derivative of xsinx is equal to d(xsinx)/dx = xcosx + sinx. We can evaluate the derivative of xsinx using the first principle and the product rule.

\int e^x\cos (x)dx \int_{0}^{\pi}\sin(x)dx \sum_{n=0}^{\infty}\frac{3}{2^n} Show More

We can find the derivatives of sin x and cos x by using the definition of derivative and the limit formulas found earlier. With these two formulas, we can determine the derivatives of all six basic …

Take the inverse tangent of both sides of the equation to extract x x from inside the tangent. x = arctan(1) x = arctan (1) Simplify the right side. Tap for more steps... The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from π π to find the solution in the fourth quadrant.

Dec 16, 2024 · Misc 17 Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): sin⁡〖x + cos⁡x 〗/sin⁡〖x − cos⁡x 〗 Let f (x) = sin⁡〖x + cos⁡x 〗/sin⁡〖x − cos⁡x 〗 Let u = sin x + cos x & v = sin x – cos x

Let f (x) = sin x − x cos x x sin x + cos x which is of the form u v f ′ ( x ) = u ′ v − v ′ u v 2 = ( x sin x + cos x ) d d x ( sin x − x cos x ) − ( sin x − x cos x ) d d x ( x sin x + cos x ) ( x sin x + cos x ) 2

The equation [1+cos(2x)]/cos x = sin (2x)/[1 - cos(2x)] can worked separately for the LHS and RHS and compared later. So starting from the LHS [1+cos(2x)]/cos x =[1 + cos^2 (x) - sin^2 (x)]/cos x ...

You should just use the summation formula for sines: \sin (x + y) = \sin (x)\cos (y) + \cos (x)\sin (y) This is how it works \eqalign { \sin (x) + \cos (x) &= \sqrt 2 \left ( { {1 \over {\sqrt 2 }}\cos (x) + {1 \over {\sqrt 2 }}\sin (x)} \right) \cr &= \sqrt 2 \left ( {\sin ( {\pi \over 4})\cos (x) + \cos ( {\pi \over 4})\sin (x)} \right) \cr &=...

Jun 11, 2018 · Put cosx = t . ⇒ dt = −sinx dx \(\therefore I =\frac \pi 2 \int\limits_1^{-1} \frac 1{1 + t^2}(-dt)\) \(= \pi \int\limits_0^1\frac 1{1 + t^2}dt\) \(= \pi \tan^{-1}1\) \(= \frac{\pi^2}4\)