Find the derivative of a function containing radicals
Let $f(x)= -7x^5 \sqrt x - \dfrac{8}{x^2 \sqrt x}$
$f'(x)=?$
Find the derivative of a function containing radicals
-1
$\begingroup$
derivatives
2 Answers
1
Hint. Observe that $$ f(x)=-7x^{5+1/2}-8x^{-2-1/2} $$ then use $$ \left(x^\alpha \right)'=\alpha \cdot x^{\alpha-1}, \qquad (u+v)'=u'+v'. $$
1
Hint -
f(x) = $-7x^5 \cdot x^{\frac12} - 8x^{-2} \cdot x^{\frac{-1}2}$
= $-7x^{5+\frac12} - 8x^{-2-\frac12}$
= $-7x^{\frac{11}2} - 8x^{\frac{-5}2}$
Now find derivative.