what is the derivative of y=(5x^4-7)^2/3 using chain rule ?
SOLUTION:
[tex] \frac{d}{dk} ( \frac{(5x {}^{4 } - 7) {}^{2} }{3} [/tex]
[tex] = \frac{40 {}^{3 } (5x {}^{4 } - 7 )}{3}[/tex]
TAKE THE CONSTANT OUT:
[tex] = \frac{1d}{3dx} ((5x {}^{4} - 7) {}^{2} )[/tex]
APPLY THE CHAIN RULE:
[tex] = 2(5x {}^{4} - 7) \frac{d}{dx} (5x {}^{4} - 7)[/tex]
[tex] \frac{d}{dx} (5x {}^{4} - 7) = 20x {}^{3} [/tex]
[tex] = \frac{1}{2} \times 2(5x {}^{4} - 7) \times 20x {}^{3} [/tex]
SIMPLIFY:
[tex] \frac{1}{3} \times 2(5x {}^{4} - 7) \times 20x {}^{3} [/tex]
[tex] \large \orange{ \boxed{= \frac{40x {}^{3}(5x {}^{4} - 7) }{3} }}[/tex]
