The function f(x) = sin x*(sin x + cos x). Use the product rule to determine the derivative of f(x).
f'(x) = (sin x)'*(sin x + cos x) + sin x*(sin x + cos x)'
f'(x) = (cos x)*(sin x + cos x) + sin x*(cos x - sin x)
= cos^2x + cos x*sin x + sin x*cos x - sin^2x
= cos^2 x - sin ^2x + 2*cos x*sin x
At x = pi/4 , the value of f'(x) = 1. The tangent at the point (pi/4, 1) has slope 1 and the equation of the tangent is : (y - 1)/(x - pi/4) = 1
y = (x - pi/4 + 1)
This can be seen in the following graph:
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