Question

Срочно Найти производную функции: 1. Y= 3x - 9cos x; 2. Y=9x5 + 2sinx - 10; 4. Y = 2.x tgx;

Answer 1

Ответ:

1

$y = 3x - 9 \cos(x)$

$y '= 3 - ( - 9 \sin(x)) = 3 + 9 \sin(x)$

2

$y = 9 {x}^{5} + 2 \sin(x) - 10$

$y '= 9 \times 5 {x}^{4} + 2 \cos(x) - 0 = \\ = 45 {x}^{4} + 2 \cos(x)$

3

$y = 2xtgx$

$y '= (2x)'tgx + (tgx) '\times 2x = \\ = 2tgx + \frac{2x}{ \cos {}^{2} (x) }$

Answer 2

Derivative of the Function Y = 3x - 9cos(x)

To find the derivative of the function Y = 3x - 9cos(x), we can use the rules of differentiation. The derivative of a constant multiplied by a variable is simply the constant, and the derivative of the cosine function is negative sine. Therefore, the derivative of Y with respect to x is:

Y' = 3 - (-9sin(x))

Simplifying further, we get:

Y' = 3 + 9sin(x)

Derivative of the Function Y = 9x^5 + 2sin(x) - 10

To find the derivative of the function Y = 9x^5 + 2sin(x) - 10, we can again use the rules of differentiation. The derivative of a power function is obtained by multiplying the coefficient by the power and reducing the power by 1. The derivative of the sine function is cosine. Therefore, the derivative of Y with respect to x is:

Y' = 45x^4 + 2cos(x)

Derivative of the Function Y = 2x + tg(x)

To find the derivative of the function Y = 2x + tg(x), we need to use the chain rule. The derivative of the tangent function is sec^2(x), and the derivative of a linear function is simply the coefficient of x. Therefore, the derivative of Y with respect to x is:

Y' = 2 + sec^2(x)

Please note that the derivative of the tangent function is often written as sec^2(x) or 1 + tan^2(x), depending on the notation used.

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