Exercise
$\frac{d}{dx}\left(3\arccot\left(2-x^2\right)-5e^{2x}+2\cos\left(x-1\right)\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the derivative d/dx(3arccot(2-x^2)-5e^(2x)2cos(x-1)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). Applying the derivative of the exponential function.
Find the derivative d/dx(3arccot(2-x^2)-5e^(2x)2cos(x-1)) using the sum rule
Final answer to the exercise
$\frac{6x}{1+\left(2-x^2\right)^2}-10e^{2x}-2\sin\left(x-1\right)$