Mathematics calculus

Question

Find the derivative of g(x) = 3 √x + csc (x).

Answer 1

To find the derivative of g(x)=3√x+csc(x), start by rewriting √x as x^1/2

So now we have g(x) = 3x^1/2 + csc(x)

Now let's take the derivative.

For the first term, we need to use the power rule: D_xxⁿ = nx^n-1

And for the second term, recall that D_xcsc(x) = -csc(x)cot(x)

So g'(x) = 3•1/2•x^1/2-1 - csc(x)cot(x)

Now let's simplify:

g'(x) = (3/2)x^-1/2 - csc(x)cot(x)

g'(x) = (3/2)•(1/x^1/2) - csc(x)cot(x)

g'(x) = 3/(2x^1/2) - csc(x)cot(x)

g'(x) = 3/(2√x) - csc(x)cot(x)