Question

Derivada de f(x)=1/3 (2x^5+6x^-3)^5 se possível com passo a passo.
Tenho o resultado de 160 (x^8+3)^4(5x^8-9)/3x^16 mas não consigo chegar

Answer 1

f(x)=1/3 (2x^5+6x^-3)^5

já seria a resposta

f'(x)=(1/3) * 5 * (2x⁵+6x⁻³)⁴ * ( 10x⁴ -18x⁻⁴)


arrumando para ficar igual a sua resposta

f'(x)=(1/3) * 5 * 2⁴ *(x⁵+3x⁻³)⁴ * ( 10x⁴ -18x⁻⁴)

f'(x)=(1/3) * 5 * 2⁴ *(x⁵+3/x³)⁴ * ( 10x⁴ -18/x⁴)

f'(x)=(1/3) * 5 * 16 *(x⁵+3/x³)⁴ * ( 10x⁴ -18/x⁴)

f'(x)=(1/3) * 5 * 16 *(1/x³)⁴ *(x⁵+3/x³)⁴ * ( 10x⁴ -18/x⁴)

f'(x)=(80/3) * (1/x¹²) (x⁸+3)⁴ * (1/x⁴)*( 10x⁸ - 18)

f'(x)=(80/3) * (1/x¹²) (x⁸+3)⁴ * (1/x⁴)*( 10x⁸ - 18)

f'(x)=(80/3) *  (x⁸+3)⁴ * ( 10x⁸ - 18) /x¹⁶

f'(x)=(80/3) *  (x⁸+3)⁴ * 2*( 5x⁸ - 9) /x¹⁶

f'(x)=(160/3) *  (x⁸+3)⁴ * ( 5x⁸ - 9) /x¹⁶

f'(x)=160 *  (x⁸+3)⁴ * ( 5x⁸ - 9) /3x¹⁶