Exercise
$\frac{d}{dx}\left(1-x\right)\tan\left(x\right)$
Step-by-step Solution
Learn how to solve differential equations problems step by step online. Find the derivative of (1-x)tan(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=1-x and g=\tan\left(x\right). The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if {f(x) = tan(x)}, then {f'(x) = sec^2(x)\cdot D_x(x)}. The derivative of the linear function is equal to 1. The derivative of a sum of two or more functions is the sum of the derivatives of each function.
Find the derivative of (1-x)tan(x)
Final answer to the exercise
$-\tan\left(x\right)+\left(1-x\right)\sec\left(x\right)^2$