What is the derivative of (6x+5^x) ?

The derivative of (6x+5^x) is (ln(6x+5)+(6x)/(6x+5))(6x+5)^x

What is the first derivative of (6x+5^x) ?

The first derivative of (6x+5^x) is (ln(6x+5)+(6x)/(6x+5))(6x+5)^x

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\frac{d}{d x} ((6 x + 5)^{x})

(ln (6 x + 5) + \frac{6 x}{6 x + 5}) (6 x + 5)^{x}

Solution steps

\frac{d}{d x} ((6 x + 5)^{x})

Apply exponent rule:

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

(6 x + 5)^{x} = e^{x l n (6 x + 5)}

= \frac{d}{d x} (e^{x l n (6 x + 5)})

Apply the chain rule:

e^{x l n (6 x + 5)} \frac{d}{d x} (x ln (6 x + 5))

= e^{x l n (6 x + 5)} \frac{d}{d x} (x ln (6 x + 5))

\frac{d}{d x} (x ln (6 x + 5)) = ln (6 x + 5) + \frac{6 x}{6 x + 5}

= e^{x l n (6 x + 5)} (ln (6 x + 5) + \frac{6 x}{6 x + 5})

e^{x l n (6 x + 5)} = (6 x + 5)^{x}

= (ln (6 x + 5) + \frac{6 x}{6 x + 5}) (6 x + 5)^{x}

\int - \frac{2}{64 - 100 x ^{2}} d x

n = 0 \sum \infty \frac{x ^{n}}{2 n !}

(2.9) (- 3.2)

- 8 x^{2}, at x = - 4

\int \frac{60 t}{m ^{0.2}} d t

What is the derivative of (6x+5^x) ?
The derivative of (6x+5^x) is (ln(6x+5)+(6x)/(6x+5))(6x+5)^x
What is the first derivative of (6x+5^x) ?
The first derivative of (6x+5^x) is (ln(6x+5)+(6x)/(6x+5))(6x+5)^x