What is the derivative of nln(0.4nx+0.6) ?

The derivative of nln(0.4nx+0.6) is (0.4n^2)/(0.4nx+0.6)

What is the first derivative of nln(0.4nx+0.6) ?

The first derivative of nln(0.4nx+0.6) is (0.4n^2)/(0.4nx+0.6)

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\frac{d}{d x} (n ln (0.4 n x + 0.6))

\frac{0.4 n ^{2}}{0.4 n x + 0.6}

Solution steps

\frac{d}{d x} (n ln (0.4 n x + 0.6))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= n \frac{d}{d x} (ln (0.4 n x + 0.6))

Apply the chain rule:

\frac{1}{0.4 n x + 0.6} \frac{d}{d x} (0.4 n x + 0.6)

= \frac{1}{0.4 n x + 0.6} \frac{d}{d x} (0.4 n x + 0.6)

\frac{d}{d x} (0.4 n x + 0.6) = 0.4 n

= n \frac{1}{0.4 n x + 0.6} \cdot 0.4 n

Simplify

n \frac{1}{0.4 n x + 0.6} \cdot 0.4 n : \frac{0.4 n ^{2}}{0.4 n x + 0.6}

= \frac{0.4 n ^{2}}{0.4 n x + 0.6}

\frac{( x ^{2} )}{8 + x}

y = x^{2}, y = 2 - x^{2}

e^{x^{5}}

y = \frac{x}{x}

What is the derivative of nln(0.4nx+0.6) ?
The derivative of nln(0.4nx+0.6) is (0.4n^2)/(0.4nx+0.6)
What is the first derivative of nln(0.4nx+0.6) ?
The first derivative of nln(0.4nx+0.6) is (0.4n^2)/(0.4nx+0.6)