f(x) = sin x cos x + x^3 tan x. Find f ' (x)

Answer 1

Use the product rule for each term of the defined function.

y' = cos(x)cos(x)+sin(x)[-sin(x)]+3x²tan(x)+x³sec²(x)

= cos²(x)-sin²(x)+3x²tan(x)+x³sec²(x)

And if you want:

= cos(2x) + 3x²tan(x)+x³sec²(x)

Here is a Desmos graph for this problem. Disable row1 and enable rows 2,3,4 to see that the derivatives are all the same. You the slider on x1 to see tangent lines to the graph at different values of x1.

desmos.com/calculator/nccwatfefi