What is the derivative of (a+2x)^{7x} ?

The derivative of (a+2x)^{7x} is 7(ln(a+2x)+(2x)/(a+2x))(a+2x)^{7x}

What is the first derivative of (a+2x)^{7x} ?

The first derivative of (a+2x)^{7x} is 7(ln(a+2x)+(2x)/(a+2x))(a+2x)^{7x}

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derivative of

(a + 2 x)^{7 x}

7 (ln (a + 2 x) + \frac{2 x}{a + 2 x}) (a + 2 x)^{7 x}

Solution steps

\frac{d}{d x} ((a + 2 x)^{7 x})

Apply exponent rule:

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

(a + 2 x)^{7 x} = e^{7 x l n (a + 2 x)}

= \frac{d}{d x} (e^{7 x l n (a + 2 x)})

Apply the chain rule:

e^{7 x l n (a + 2 x)} \frac{d}{d x} (7 x ln (a + 2 x))

= e^{7 x l n (a + 2 x)} \frac{d}{d x} (7 x ln (a + 2 x))

\frac{d}{d x} (7 x ln (a + 2 x)) = 7 (ln (a + 2 x) + \frac{2 x}{a + 2 x})

= e^{7 x l n (a + 2 x)} \cdot 7 (ln (a + 2 x) + \frac{2 x}{a + 2 x})

e^{7 x l n (a + 2 x)} = (a + 2 x)^{7 x}

= 7 (ln (a + 2 x) + \frac{2 x}{a + 2 x}) (a + 2 x)^{7 x}

What is the derivative of (a+2x)^{7x} ?
The derivative of (a+2x)^{7x} is 7(ln(a+2x)+(2x)/(a+2x))(a+2x)^{7x}
What is the first derivative of (a+2x)^{7x} ?
The first derivative of (a+2x)^{7x} is 7(ln(a+2x)+(2x)/(a+2x))(a+2x)^{7x}