f(x)=12xe⋅6xMultiply&nbsp;6&nbsp;by&nbsp;12.ddx[72xe⋅x]Raise&nbsp;x&nbsp;to the power of&nbsp;1.ddx[72(x1xe)]Use the power rule&nbsp;aman=am+n&nbsp;to combine exponents.ddx[72x1+e]Since&nbsp;72&nbsp;is constant with respect to&nbsp;x, the derivative of&nbsp;72x1+e&nbsp;with respect to&nbsp;x&nbsp;is&nbsp;72ddx[x1+e].72ddx[x1+e]Differentiate using the Power Rule which states that&nbsp;ddx[xn]&nbsp;is&nbsp;nxn-1&nbsp;where&nbsp;n=1+e.72((1+e)x1+e-1)Simplify by subtracting numbers.72((1+e)xe)Simplify.Apply the distributive property.(72⋅1+72e)xeApply the distributive property.72⋅1xe+72exeMultiply&nbsp;72&nbsp;by&nbsp;1.72xe+72exeReorder terms.72exe+72xe&nbsp;- Answer

Expert Answer to "f(x) = 12 xe6x"

Answered question

2022-03-31

f(x) = 12 xe6x

Answer & Explanation

user_27qwe

Skilled2022-04-21Added 375 answers

$f (x) = 12 x^{e} \cdot 6 x$

Multiply $6$ by $12$ .

$\frac{d}{d x} [72 x^{e} \cdot x]$

Raise $x$ to the power of $1$ .

$\frac{d}{d x} [72 (x^{1} x^{e})]$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{d}{d x} [72 x^{1 + e}]$

Since $72$ is constant with respect to $x$ , the derivative of $72 x^{1 + e}$ with respect to $x$ is $72 \frac{d}{d x} [x^{1 + e}]$ .

$72 \frac{d}{d x} [x^{1 + e}]$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1 + e$ .

$72 ((1 + e) x^{1 + e - 1})$

Simplify by subtracting numbers.

$72 ((1 + e) x^{e})$

Simplify.

Apply the distributive property.

$(72 \cdot 1 + 72 e) x^{e}$

Apply the distributive property.

$72 \cdot 1 x^{e} + 72 e x^{e}$

Multiply $72$ by $1$ .

$72 x^{e} + 72 e x^{e}$

Reorder terms.

$72 e x^{e} + 72 x^{e}$ - Answer

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