Question #64342

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Answer 1 · 2017-07-30T00:16:57

$d/(dx) [3(sqrtx)^2 · (3x^2-1)+5x^3] = color(blue)(ul(42x^2 - 3$

We're asked to find the derivative

$d/(dx) [3(sqrtx)^2 · (3x^2-1)+5x^3]$

which is the same as

$d/(dx) [3x(3x^2-1)+5x^3]$

Using the power rule on $5x^3$ , and factoring out the constant, $3$ :

$= 15x^2 + 3d/(dx)[x(3x^2-1)]$

Using the product rule, which is

$d/(dx)[uv] = v(du)/(dx) + u(dv)/(dx)$

where

$u = x$

$v = 3x^2-1$ :

$= 15x^2 + 3((3x^2-1)d/(dx)[x] + xd/(dx)[3x^2-1])$

The derivative of $x$ is $1$ , and the derivative of $3x^2-1$ is $6x$ (both from power rule):

$= 15x^2 + 3((3x^2-1)(1) + x(6x))$

$= 15x^2 + 9x^2 - 3 + 18x^2$

$= color(blue)(ul(42x^2-3$

At least two other calculators agree with me, so the given answer must be incorrect...maybe you were doing it right after all!