Differentiate the function \( G(x)=-7 \sqrt{x} \sec x \)

To differentiate the function \( G(x) = -7 \sqrt{x} \sec x \), we can use the product rule since it is the product of two functions: \( -7 \sqrt{x} \) and \( \sec x \). First, let's find the derivatives of each part: 1. The derivative of \( -7 \sqrt{x} \) is \( -\frac{7}{2\sqrt{x}} \). 2. The derivative of \( \sec x \) is \( \sec x \tan x \). Now, applying the product rule \( (uv)' = u'v + uv' \): \[ G'(x) = \left(-\frac{7}{2\sqrt{x}}\right) \sec x + (-7\sqrt{x})(\sec x \tan x) \] Putting it all together, we get: \[ G'(x) = -\frac{7}{2\sqrt{x}} \sec x - 7\sqrt{x} \sec x \tan x \] That’s the derivative of \( G(x) \)!