Question

Срочно,пожалуйста!Найти производные функций:а)f(x)=sin(п/2-альфа)*х^2+sin(- п/4)*x

Answer 1

А)f(x)=sin(π/2-x)*x²+sin(-π/4)*x=cosx *x²-√2/2*x
f`(x)=-sinx*x²+2x*cosx-√2/2

Answer 2

Calculating the Derivative of f(x)

To find the derivative of the function f(x) = sin(π/2 - α) * x^2 + sin(-π/4) * x, we can use the rules of differentiation. Let's break down the function and find the derivative step by step.

1. The first term of the function is sin(π/2 - α) * x^2. To find its derivative, we can use the chain rule. The derivative of sin(u) is cos(u), and the derivative of x^2 is 2x. Applying the chain rule, we get:

d/dx [sin(π/2 - α) * x^2] = cos(π/2 - α) * 2x

2. The second term of the function is sin(-π/4) * x. The derivative of sin(u) is cos(u), and the derivative of x is 1. So, the derivative of this term is:

d/dx [sin(-π/4) * x] = cos(-π/4) * 1

Now, let's simplify the derivatives we found:

d/dx [sin(π/2 - α) * x^2] = cos(π/2 - α) * 2x

d/dx [sin(-π/4) * x] = cos(-π/4) * 1

Therefore, the derivative of the function f(x) = sin(π/2 - α) * x^2 + sin(-π/4) * x is:

f'(x) = cos(π/2 - α) * 2x + cos(-π/4)

Please note that the derivative is expressed in terms of the variable x. The values of α and π are constants.

I hope this helps! Let me know if you have any further questions.