What is the derivative of ln(1+3x+xln(x)) ?

The derivative of ln(1+3x+xln(x)) is 3/(1+3x)+ln(x)+1

What is the first derivative of ln(1+3x+xln(x)) ?

The first derivative of ln(1+3x+xln(x)) is 3/(1+3x)+ln(x)+1

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\frac{d}{d x} (ln (1 + 3 x) + x ln (x))

\frac{3}{1 + 3 x} + ln (x) + 1

Solution steps

\frac{d}{d x} (ln (1 + 3 x) + x ln (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (ln (1 + 3 x)) + \frac{d}{d x} (x ln (x))

\frac{d}{d x} (ln (1 + 3 x)) = \frac{3}{1 + 3 x}

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

= \frac{3}{1 + 3 x} + ln (x) + 1

\frac{d}{d x} (3 x (x^{3} - 1))

\frac{d}{d x} (\frac{1}{( 3 x ^{2} + x + 2 ) ^{5}})

\int \frac{- 10}{( x - 2 ) ( x ^{2} + 4 )} d x

\int \frac{tan ^{4} ( x )}{sec ^{5} ( x )} d x

y^{^{'}} = 4 y^{2} x

What is the derivative of ln(1+3x+xln(x)) ?
The derivative of ln(1+3x+xln(x)) is 3/(1+3x)+ln(x)+1
What is the first derivative of ln(1+3x+xln(x)) ?
The first derivative of ln(1+3x+xln(x)) is 3/(1+3x)+ln(x)+1