Question

Question 1- Whats the derivative of: A) f(x)= 4 cos(x) + ln(x+1) B) f(x)= sec(x) X tg(x)

Answer 1

The derivatives for this problem are given as follows:

a) $f^{\prime}(x) = -4\sin{x} + \frac{1}{x + 1}$

b) $f^{\prime}(x) = \sec{x}\tan^{2}{x} + \sec^3{x}$.

What is the derivative of the sum?

The derivative of the sum is the sum of the derivatives.

In this problem, the function is:

$f(x) = 4\cos{x} + \ln{(x + 1)}$

Using a derivative table for the derivatives of the cosine and the ln, the derivative of the function is:

$f^{\prime}(x) = (4\cos{x})^{\prime} + (\ln{(x + 1)})^{\prime}$

$f^{\prime}(x) = -4\sin{x} + \frac{1}{x + 1}$

What is the product rule?

The derivative of the product is given as follows:

$(f(x) \times g(x))^{\prime} = f^{\prime}(x)g(x) + g^{\prime}(x)f(x)$

In this problem, we have that:

• $f(x) = \sec{x}, f^{\prime}(x) = \sec{x}\tan{x}$.

• $g(x) = \tan{x}, f^{\prime}(x) = \sec^2{x}$.

Hence the derivative is:

$f^{\prime}(x) = \sec{x}\tan^{2}{x} + \sec^3{x}$.

More can be learned about derivatives at brainly.com/question/2256078

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