Question

((3x+7)*(7x^3+5x-4))'

Answer 1

Ответ: 21х^4 +49х^3 +15х^2 +23х-28

Answer 2

To find the derivative of the expression ((3x+7)*(7x^3+5x-4))', we can apply the product rule of differentiation. The product rule states that the derivative of a product of two functions is given by:

(fg)' = f'g + fg'

Let's differentiate the expression step by step:

First, let's find the derivative of the first function: (3x+7). The derivative of 3x+7 with respect to x is simply 3.

Next, let's find the derivative of the second function: (7x^3+5x-4). To differentiate this function, we apply the power rule and sum rule:

The power rule states that the derivative of x^n with respect to x is nx^(n-1). For the term 7x^3, the derivative is: (7 * 3)x^(3-1) = 21x^2.

For the term 5x, the derivative is simply 5.

And for the constant term -4, the derivative is 0 since the derivative of a constant is always 0.

Now, we can apply the product rule using the derivatives we found:

((3x+7)*(7x^3+5x-4))' = (3x+7)' * (7x^3+5x-4) + (3x+7) * (7x^3+5x-4)'

Simplifying further:

= (3 * 1) * (7x^3+5x-4) + (3x+7) * (21x^2 + 5)

= 21x^3 + 15x - 12 + (63x^3 + 35x^2 + 15x + 147)

Combining like terms:

= 84x^3 + 35x^2 + 30x + 135

Therefore, the derivative of ((3x+7)*(7x^3+5x-4)) with respect to x is 84x^3 + 35x^2 + 30x + 135.