What is the derivative of (5x+4)^x ?

The derivative of (5x+4)^x is (ln(5x+4)+(5x)/(5x+4))(5x+4)^x

What is the first derivative of (5x+4)^x ?

The first derivative of (5x+4)^x is (ln(5x+4)+(5x)/(5x+4))(5x+4)^x

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derivative of

(5 x + 4)^{x}

(ln (5 x + 4) + \frac{5 x}{5 x + 4}) (5 x + 4)^{x}

Solution steps

\frac{d}{d x} ((5 x + 4)^{x})

Apply exponent rule:

a^{b} = e^{b l n (a)}

(5 x + 4)^{x} = e^{x l n (5 x + 4)}

= \frac{d}{d x} (e^{x l n (5 x + 4)})

Apply the chain rule:

e^{x l n (5 x + 4)} \frac{d}{d x} (x ln (5 x + 4))

= e^{x l n (5 x + 4)} \frac{d}{d x} (x ln (5 x + 4))

\frac{d}{d x} (x ln (5 x + 4)) = ln (5 x + 4) + \frac{5 x}{5 x + 4}

= e^{x l n (5 x + 4)} (ln (5 x + 4) + \frac{5 x}{5 x + 4})

e^{x l n (5 x + 4)} = (5 x + 4)^{x}

= (ln (5 x + 4) + \frac{5 x}{5 x + 4}) (5 x + 4)^{x}

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\frac{d}{d x} (\frac{3 x ^{2}}{2} - \frac{7}{5 x ^{2}})

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What is the derivative of (5x+4)^x ?
The derivative of (5x+4)^x is (ln(5x+4)+(5x)/(5x+4))(5x+4)^x
What is the first derivative of (5x+4)^x ?
The first derivative of (5x+4)^x is (ln(5x+4)+(5x)/(5x+4))(5x+4)^x