What is dy/dx (derivative) if $y=(3 + x^2)^15$ ?

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Answer 1 · 2015-03-27T03:09:32

$(dy)/(dx)=30x(3+x^2)^14$

Solution

You'll need the power rule: $d/(dx)(x^n) = n x^(n-1)$
and the chain rule.
(This combination is sometimes called the generalized power rule.)

$d/(dx)[(g(x))^n]=n(g(x))^(n-1)*g'(x)$

or $d/(dx)(u^n) = n u^(n-1) (du)/(dx)$

$d/(dx)((3+x^2)^15)=15(3+x^2)^14*2x=30x(3+x^2)^14$

What is dy/dx (derivative) if y=(3 + x^2)^15y=(3 + x^2)^15?