What is the derivative of (1+2x^{ln(x)}) ?

The derivative of (1+2x^{ln(x)}) is x^{ln(1+2x)}((ln(1+2x))/x+(2ln(x))/(1+2x))

What is the first derivative of (1+2x^{ln(x)}) ?

The first derivative of (1+2x^{ln(x)}) is x^{ln(1+2x)}((ln(1+2x))/x+(2ln(x))/(1+2x))

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\frac{d}{d x} ((1 + 2 x)^{l n (x)})

x^{l n (1 + 2 x)} (\frac{ln ( 1 + 2 x )}{x} + \frac{2 ln ( x )}{1 + 2 x})

Solution steps

\frac{d}{d x} ((1 + 2 x)^{l n (x)})

Apply exponent rule:

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

(1 + 2 x)^{l n (x)} = e^{l n (x) l n (1 + 2 x)}

= \frac{d}{d x} (e^{l n (x) l n (1 + 2 x)})

Apply the chain rule:

e^{l n (x) l n (1 + 2 x)} \frac{d}{d x} (ln (x) ln (1 + 2 x))

= e^{l n (x) l n (1 + 2 x)} \frac{d}{d x} (ln (x) ln (1 + 2 x))

\frac{d}{d x} (ln (x) ln (1 + 2 x)) = \frac{ln ( 1 + 2 x )}{x} + \frac{2 ln ( x )}{1 + 2 x}

= e^{l n (x) l n (1 + 2 x)} (\frac{ln ( 1 + 2 x )}{x} + \frac{2 ln ( x )}{1 + 2 x})

e^{l n (x) l n (1 + 2 x)} = x^{l n (1 + 2 x)}

= x^{l n (1 + 2 x)} (\frac{ln ( 1 + 2 x )}{x} + \frac{2 ln ( x )}{1 + 2 x})

h \to 0 lim (\frac{0}{h})

\frac{s}{( s ^{2} + 4 ^{2} ) ^{2}}

\int sin (n x + x) d x

\frac{\partial}{\partial x} (8 e^{x^{6} y})

\int x^{5} x^{6} + 8 d x

What is the derivative of (1+2x^{ln(x)}) ?
The derivative of (1+2x^{ln(x)}) is x^{ln(1+2x)}((ln(1+2x))/x+(2ln(x))/(1+2x))
What is the first derivative of (1+2x^{ln(x)}) ?
The first derivative of (1+2x^{ln(x)}) is x^{ln(1+2x)}((ln(1+2x))/x+(2ln(x))/(1+2x))