5 months ago
Q:

(-3x+(x^2+5)^3)^2 Calculate derivative

Accepted Solution

A:
$f '\left( x \right)=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( {\left( -3x+{\left( {x}^{2}+5 \right)}^{3} \right)}^{2} \right)$
$f '\left( x \right)=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( {\left( -3x+{x}^{6}+15{x}^{4}+75{x}^{2}+125 \right)}^{2} \right)$
$f '\left( x \right)=\frac{ \mathrm{d} }{ \mathrm{d}g} \left( {g}^{2} \right) \times \frac{ \mathrm{d} }{ \mathrm{d}x} \left( -3x+{x}^{6}+15{x}^{4}+75{x}^{2}+125 \right)$
$f '\left( x \right)=2g \times \frac{ \mathrm{d} }{ \mathrm{d}x} \left( -3x+{x}^{6}+15{x}^{4}+75{x}^{2}+125 \right)$
$f '\left( x \right)=2g \times \left( -3+6{x}^{5}+15 \times 4{x}^{3}+75 \times 2x \right)$
$f '\left( x \right)=2\left( -3x+{x}^{6}+15{x}^{4}+75{x}^{2}+125 \right) \times \left( -3+6{x}^{5}+15 \times 4{x}^{3}+75 \times 2x \right)$
$f '\left( x \right)=37518x-42{x}^{6}-450{x}^{4}-1350{x}^{2}+12{x}^{11}+300{x}^{9}+3000{x}^{7}+15000{x}^{5}+37500{x}^{3}-750$