What is the derivative of (e^x+1^{7x}) ?

The derivative of (e^x+1^{7x}) is 7(ln(e^x+1)+(e^xx)/(e^x+1))(e^x+1)^{7x}

What is the first derivative of (e^x+1^{7x}) ?

The first derivative of (e^x+1^{7x}) is 7(ln(e^x+1)+(e^xx)/(e^x+1))(e^x+1)^{7x}

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\frac{d}{d x} ((e^{x} + 1)^{7 x})

7 (ln (e^{x} + 1) + \frac{e ^{x} x}{e ^{x} + 1}) (e^{x} + 1)^{7 x}

Solution steps

\frac{d}{d x} ((e^{x} + 1)^{7 x})

Apply exponent rule:

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

(e^{x} + 1)^{7 x} = e^{7 x l n (e^{x} + 1)}

= \frac{d}{d x} (e^{7 x l n (e^{x} + 1)})

Apply the chain rule:

e^{7 x l n (e^{x} + 1)} \frac{d}{d x} (7 x ln (e^{x} + 1))

= e^{7 x l n (e^{x} + 1)} \frac{d}{d x} (7 x ln (e^{x} + 1))

\frac{d}{d x} (7 x ln (e^{x} + 1)) = 7 (ln (e^{x} + 1) + \frac{e ^{x} x}{e ^{x} + 1})

= e^{7 x l n (e^{x} + 1)} \cdot 7 (ln (e^{x} + 1) + \frac{e ^{x} x}{e ^{x} + 1})

e^{7 x l n (e^{x} + 1)} = (e^{x} + 1)^{7 x}

= 7 (ln (e^{x} + 1) + \frac{e ^{x} x}{e ^{x} + 1}) (e^{x} + 1)^{7 x}

\frac{\partial}{\partial x} (- x + y + 2)

\frac{d}{d x} (cos (4 x - \frac{π}{3}))

\int ln (5 x) d x

\int x^{2} e^{- \frac{x ^{2}}{2}} d x

x \to \frac{π}{2} lim (2 e^{x} cos (x))

What is the derivative of (e^x+1^{7x}) ?
The derivative of (e^x+1^{7x}) is 7(ln(e^x+1)+(e^xx)/(e^x+1))(e^x+1)^{7x}
What is the first derivative of (e^x+1^{7x}) ?
The first derivative of (e^x+1^{7x}) is 7(ln(e^x+1)+(e^xx)/(e^x+1))(e^x+1)^{7x}