Question

Помогите пожалуйста :((( Найдите производную: 1) f(x)=8x^4-1/x^2+x*√x-2 2) f(x)=1+3x/1-3x 3) f(x)=7x^3+2/x^2-x^2*√x+3 4) f(x)=2-5x^2/2+3x Прошу очень надо :'((((((((

Answer 1

1.F'(x)=0-1/2*(-sin8x)*8=4sin 8x

Answer 2

Производные функций:

1) f(x) = 8x^4 - 1/x^2 + x√x - 2

To find the derivative of this function, we can apply the power rule and the product rule.

Using the power rule, the derivative of x^n with respect to x is nx^(n-1).

Let's find the derivatives of each term separately:

The derivative of 8x^4 is 32x^3.

The derivative of 1/x^2 is (-2/x^3) using the power rule.

The derivative of x√x is (1/2)x^(-1/2) + (1/2)x^(1/2) using the product rule.

The derivative of 2 is 0 since it is a constant.

Now, let's add up the derivatives:

f'(x) = 32x^3 - 2/x^3 + (1/2)x^(-1/2) + (1/2)x^(1/2) + 0

Simplifying this expression, we get:

f'(x) = 32x^3 - 2/x^3 + (1/2)x^(-1/2) + (1/2)x^(1/2)

2) f(x) = 1 + 3x / (1 - 3x + 3)

To find the derivative of this function, we can apply the quotient rule.

The quotient rule states that if we have a function u(x) divided by v(x), the derivative is given by:

(u'v - uv') / v^2

Let's differentiate each part of the function:

The derivative of 1 is 0 since it is a constant.

The derivative of 3x is 3.

The derivative of 1 - 3x + 3 is -3.

Now, using the quotient rule, we have:

f'(x) = (3(1 - 3x + 3) - (1 + 3x)(-3)) / (1 - 3x + 3)^2

Simplifying this expression, we get:

f'(x) = (9 - 9x - 9 + 3x) / (1 - 3x + 3)^2 = (-6x) / (1 - 3x + 3)^2

3) f(x) = 7x^3 + 2 / x^2 - x^2√x + 3

To find the derivative of this function, we can apply the power rule and the product rule.

Using the power rule, the derivative of x^n with respect to x is nx^(n-1).

Let's find the derivatives of each term separately:

The derivative of 7x^3 is 21x^2.

The derivative of 2 is 0 since it is a constant.

The derivative of x^2 is 2x.

The derivative of -x^2√x is (-2x^2/x)(1/2) + (-x^2)(1/2)(1/x) using the product rule and the chain rule.

The derivative of 3 is 0 since it is a constant.

Now, let's add up the derivatives:

f'(x) = 21x^2 + 0 + 2x - (x^2)(1/√x) - x^2(1/2)(1/x)

Simplifying this expression, we get:

f'(x) = 21x^2 + 2x - x√x - (1/2)x

4) f(x) = 2 - 5x^2 / (2 + 3x)

To find the derivative of this function, we can apply the quotient rule.

Let's differentiate each part of the function:

The derivative of 2 is 0 since it is a constant.

The derivative of -5x^2 is -10x.

The derivative of 2 + 3x is 3.

Now, using the quotient rule, we have:

f'(x) = ((-10x)(2 + 3x) - (-5x^2)(3)) / (2 + 3x)^2

Simplifying this expression, we get:

f'(x) = (-20x - 30x^2 + 15x^2) / (2 + 3x)^2 = (-30x^2 - 20x) / (2 + 3x)^2

Я надеюсь, что эти подробные ответы помогут вам! Если у вас есть дополнительные вопросы, пожалуйста, не стесняйтесь задавать их!