Question

encontre a derivada da quarta função f(x)= x^4 +6x^2 -9

Answer 1

Derivada de primeira ordem:

$\mathsf{f(x)=x^{4}+6x^{2}-9}}}\\\\\\\\ \mathsf{f'(x)=4x^{4-1}+2~\cdot~6x^{2-1}}}\\\\\\\\\ \large\boxed{\boxed{\boxed{\mathsf{f'(x)=4x^{3}+12x}}}}}}}}}}}}}}}$

Derivada de segunda ordem:

$\mathsf{f(x)=x^{4}+6x^{2}-9}}}\\\\\\\\\ \mathsf{f''(x)=3~\cdot~4x^{3-1}+1}}}\\\\\\\\\ \large\boxed{\boxed{\boxed{\mathsf{f''(x)=12x^{2}+1}}}}}}}}}}}}}}}}$

Derivada de terceira ordem:

$\mathsf{f(x)=x^{4}+6x^{2}-9}}}\\\\\\\\ \mathsf{f'''(x)=2~\cdot~12x^{2-1}}}\\\\\\\\\ \large\boxed{\boxed{\mathsf{f'''(x)=24x}}}}}}}}$

Derivada de quarta ordem:

$\mathsf{f(x)=x^{4}+6x^{2}-9}}}\\\\\\\ \mathsf{f''''(x)=1}}}}}}}}}}}}$

Espero que te ajude. '-'