Question

Вычислите значение производной функции f(x)=(3х+5)×cosx в точке х=пи на 6 .срочно пожалуйста на листочке с решением.буду очень благодарна;) ​

Answer 1

Ответ:

Объяснение:

f'(x)=(3x+5)'×cosx+(cosx)'×(3x+5)=3*cosx-sinx*(3x+5)

f'(П/6)=3*√3/2-1/2(3П/6+5)=3√3/2-(П+10)/4=

=(6√3-10-П)/4≈-0,69

Answer 2

f(x)=(3х+5)×cosx

f'(x)=(3х+5)'×cosx+ (3х+5)×(cosx)'=3×cosx+(3х+5)×(-sinx)=

=3×cosx-(3х+5)×sinx

$f'(\frac{\pi }{6} )=3*cos\frac{\pi }{6} -(3x+5)*sin\frac{\pi }{6} =3*\frac{\sqrt{3} }{2} -\frac{1}{2} *(3*\frac{\pi }{6} +5)$ =$\frac{3\sqrt{3} }{2} -\frac{\pi }{4} -\frac{5}{2}$

Answer 3

Calculation of the Derivative

To calculate the value of the derivative of the function f(x) = (3x + 5) * cos(x) at the point x = π/6, we need to find the derivative of the function and then substitute the given value of x.

The derivative of a function can be found using the product rule and the chain rule. The product rule states that the derivative of the product of two functions is equal to the derivative of the first function times the second function, plus the first function times the derivative of the second function.

In this case, we have the function f(x) = (3x + 5) * cos(x). Applying the product rule, we get:

f'(x) = (3x + 5) * (-sin(x)) + cos(x) * 3

Simplifying this expression, we have:

f'(x) = -3sin(x) + 3cos(x)

Now, we can substitute the value x = π/6 into the derivative expression to find the value of the derivative at that point:

f'(π/6) = -3sin(π/6) + 3cos(π/6)

Using the trigonometric values for sin(π/6) and cos(π/6), we can evaluate the expression:

f'(π/6) = -3 * (1/2) + 3 * (√3/2)

Simplifying further, we have:

f'(π/6) = -3/2 + 3√3/2

Therefore, the value of the derivative of the function f(x) = (3x + 5) * cos(x) at the point x = π/6 is -3/2 + 3√3/2.

Please note that the provided sources did not contain any relevant information for this specific calculation.