What is the derivative of (6x+7)^x ?

The derivative of (6x+7)^x is (ln(6x+7)+(6x)/(6x+7))(6x+7)^x

What is the first derivative of (6x+7)^x ?

The first derivative of (6x+7)^x is (ln(6x+7)+(6x)/(6x+7))(6x+7)^x

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derivative of

(6 x + 7)^{x}

(ln (6 x + 7) + \frac{6 x}{6 x + 7}) (6 x + 7)^{x}

Solution steps

\frac{d}{d x} ((6 x + 7)^{x})

Apply exponent rule:

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

(6 x + 7)^{x} = e^{x l n (6 x + 7)}

= \frac{d}{d x} (e^{x l n (6 x + 7)})

Apply the chain rule:

e^{x l n (6 x + 7)} \frac{d}{d x} (x ln (6 x + 7))

= e^{x l n (6 x + 7)} \frac{d}{d x} (x ln (6 x + 7))

\frac{d}{d x} (x ln (6 x + 7)) = ln (6 x + 7) + \frac{6 x}{6 x + 7}

= e^{x l n (6 x + 7)} (ln (6 x + 7) + \frac{6 x}{6 x + 7})

e^{x l n (6 x + 7)} = (6 x + 7)^{x}

= (ln (6 x + 7) + \frac{6 x}{6 x + 7}) (6 x + 7)^{x}

\frac{d}{d x} (x^{2} arccos (x))

\int \frac{11 x + 17}{2 x ^{2} + 7 x - 4} d x

\int \frac{1}{3 x + 7 x} d x

\int \frac{8 - x ^{2}}{9} d x

x \to 2 lim (4 x - x^{2})

What is the derivative of (6x+7)^x ?
The derivative of (6x+7)^x is (ln(6x+7)+(6x)/(6x+7))(6x+7)^x
What is the first derivative of (6x+7)^x ?
The first derivative of (6x+7)^x is (ln(6x+7)+(6x)/(6x+7))(6x+7)^x