Calculate: y=(7x-5)^4

Expression: $y={\left( 7x-5 \right)}^{4}$

Take the derivative of both sides

$y '=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( {\left( 7x-5 \right)}^{4} \right)$

Use the chain rule $\frac{ \mathrm{d} }{ \mathrm{d}x} \left( f\left( g \right) \right)=\frac{ \mathrm{d} }{ \mathrm{d}g} \left( f\left( g \right) \right) \times \frac{ \mathrm{d} }{ \mathrm{d}x} \left( g \right)$, where $g=7x-5$, to find the derivative

$y '=\frac{ \mathrm{d} }{ \mathrm{d}g} \left( {g}^{4} \right) \times \frac{ \mathrm{d} }{ \mathrm{d}x} \left( 7x-5 \right)$

Find the derivative

$y '=4{g}^{3} \times \frac{ \mathrm{d} }{ \mathrm{d}x} \left( 7x-5 \right)$

Find the derivative of the sum or difference

$y '=4{g}^{3} \times 7$

Substitute back $g=7x-5$

$y '=4{\left( 7x-5 \right)}^{3} \times 7$

Calculate the product

$y '=28{\left( 7x-5 \right)}^{3}$