What is the derivative of 10^{xln(x-x}) ?

The derivative of 10^{xln(x-x}) is ln(10)*10^{xln(x)-x}ln(x)

What is the first derivative of 10^{xln(x-x}) ?

The first derivative of 10^{xln(x-x}) is ln(10)*10^{xln(x)-x}ln(x)

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\frac{d}{d x} (1 0^{x l n (x) - x})

ln (10) \cdot 1 0^{x l n (x) - x} ln (x)

Solution steps

\frac{d}{d x} (1 0^{x l n (x) - x})

Apply exponent rule:

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

1 0^{x l n (x) - x} = e^{(x l n (x) - x) l n (10)}

= \frac{d}{d x} (e^{(x l n (x) - x) l n (10)})

Apply the chain rule:

e^{(x l n (x) - x) l n (10)} \frac{d}{d x} ((x ln (x) - x) ln (10))

= e^{(x l n (x) - x) l n (10)} \frac{d}{d x} ((x ln (x) - x) ln (10))

\frac{d}{d x} ((x ln (x) - x) ln (10)) = ln (10) ln (x)

= e^{(x l n (x) - x) l n (10)} ln (10) ln (x)

e^{(x l n (x) - x) l n (10)} = 1 0^{x l n (x) - x}

= ln (10) \cdot 1 0^{x l n (x) - x} ln (x)

\int 2 e^{x} sin (x) d x

x \to 0 lim ((- 3 x + 1)^{\frac{5}{x}})

\int (x + 2)^{13} d x

f (x) = x^{2} - 3 x

\frac{d}{d x} (\frac{x - 7 x x}{x})

What is the derivative of 10^{xln(x-x}) ?
The derivative of 10^{xln(x-x}) is ln(10)*10^{xln(x)-x}ln(x)
What is the first derivative of 10^{xln(x-x}) ?
The first derivative of 10^{xln(x-x}) is ln(10)*10^{xln(x)-x}ln(x)