Question

Differentiate with respect to x:f(x)=(ax3+bx)

3ax2+b
ax^2+b
3x^2+1
3ax^2+x

Answer 1

Answer on Question #47146 – Math – Differential Calculus | Equations

Differentiate with respect to $x$: $f(x) = (ax^3 + bx)$

$$\begin{array}{l} 3ax^2 + b \\ ax^2 + b \\ 3x^2 + 1 \\ 3ax^2 + x \\ \end{array}$$

Solution

Using formulae $(x^n)' = nx^{n-1}$, $(f(x) + g(x))' = f'(x) + g'(x)$, $(af(x))' = a \cdot f'(x)$, calculate

$$(ax^3 + bx)' = (ax^3)' + (bx)' = 3ax^2 + b.$$

Answer: $3ax^2 + b$

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