Question

Findf(x)=(7x^4−5x^3)

7x^4−5x^3
28x^3−15x^2
28x^2−15x^2
7x^3−15x^2

Answer 1

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Answer on Question #47142 – Math – Differential Calculus | Equations

Find derivative of $f(x) = (7x^4 - 5x^3)$ with respect to $x$

$$\begin{array}{l} 7x^4 - 5x^3 \\ 28x^3 - 15x^2 \\ 28x^2 - 15x^2 \\ 7x^3 - 15x^2 \\ \end{array}$$

Solution

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

calculate

$$(7x^4 - 5x^3)^\prime = (7x^4)^\prime - (5x^3)^\prime = 7 \cdot 4 \cdot x^3 - 5 \cdot 3 \cdot x^2 = 28x^3 - 15x^2.$$

Answer: $28x^3 - 15x^2$