Question

what is the derivative of f(x)=x(2x-3)^2

Answer 1

f(x)=x(2x-3)^2 = x(2x-3)(2x-3) = x(4x^2-6x-6x+9)=4x^3-6x^2-6x^2+9x=4x^3-12x^2+9x

then derivative of f(x) = 4x^3-12x^2+9x
d/dx(4x^3-12x^2+9x) = 12x^2 -24x+9

Answer 2

you gotta use power and product rules

Answer 3

that's first derivative

Answer 4

Thank you so much can you solve it with the easier way ?

Answer 5

\[\frac{ d f(x) }{ dx } = \frac{ d }{ dx } \left( x(2x-3)^2 \right) = \frac{ d }{ dx } \left( 4x^3-12x^2+9x \right) \]
\[= \frac{ d }{ dx }\left( 4x^3 \right)-\frac{ d }{ dx }\left( 12x^2 \right)+\frac{ d }{ dx }\left( 9x \right)\]
\[= (4 \times 3) x^{3-1} - (12 \times 2) x^{2-1} + (9 \times 1) x^{1-1} \]
\[= 12x^2 - 12x + 9\]

Remember that \[\frac{ d }{ dx } \left( x^{n} \right) = nx^{n-1}\]
or
\[\frac{ d }{ dx } \left( k x^{n} \right) = (n \times k) x^{n-1}\]
get it?