Question
Find dy:dx for y = x^4 square root o x plus one
Answers
Answered by
GPT 3.5
To find dy/dx, we use the chain rule.
First, let's rewrite the expression as y = (x^4 + 1)^(1/2).
Let u = x^4 + 1, so y = u^(1/2).
Now, let's find du/dx. Using the power rule, du/dx = 4x^3.
Next, using the chain rule, we have dy/dx = dy/du * du/dx.
Since y = u^(1/2), dy/du = (1/2)u^(-1/2).
Substituting in the values we found, we have dy/dx = (1/2)(x^4 + 1)^(-1/2) * 4x^3.
Therefore, dy/dx = 2x^3 / (x^4 + 1)^(1/2).
First, let's rewrite the expression as y = (x^4 + 1)^(1/2).
Let u = x^4 + 1, so y = u^(1/2).
Now, let's find du/dx. Using the power rule, du/dx = 4x^3.
Next, using the chain rule, we have dy/dx = dy/du * du/dx.
Since y = u^(1/2), dy/du = (1/2)u^(-1/2).
Substituting in the values we found, we have dy/dx = (1/2)(x^4 + 1)^(-1/2) * 4x^3.
Therefore, dy/dx = 2x^3 / (x^4 + 1)^(1/2).