What is the derivative of ln(5bx^3-3sqrt(x)) ?

The derivative of ln(5bx^3-3sqrt(x)) is (30bx^2sqrt(x)-3)/(2sqrt(x)(5bx^3-3\sqrt{x))}

What is the first derivative of ln(5bx^3-3sqrt(x)) ?

The first derivative of ln(5bx^3-3sqrt(x)) is (30bx^2sqrt(x)-3)/(2sqrt(x)(5bx^3-3\sqrt{x))}

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\frac{d}{d x} (ln (5 b x^{3} - 3 x))

\frac{30 b x ^{2} x - 3}{2 x ( 5 b x ^{3} - 3 x )}

Solution steps

\frac{d}{d x} (ln (5 b x^{3} - 3 x))

Apply the chain rule:

\frac{1}{5 b x ^{3} - 3 x} \frac{d}{d x} (5 b x^{3} - 3 x)

= \frac{1}{5 b x ^{3} - 3 x} \frac{d}{d x} (5 b x^{3} - 3 x)

\frac{d}{d x} (5 b x^{3} - 3 x) = 15 b x^{2} - \frac{3}{2 x}

= \frac{1}{5 b x ^{3} - 3 x} (15 b x^{2} - \frac{3}{2 x})

Simplify

\frac{1}{5 b x ^{3} - 3 x} (15 b x^{2} - \frac{3}{2 x}) : \frac{30 b x ^{2} x - 3}{2 x ( 5 b x ^{3} - 3 x )}

= \frac{30 b x ^{2} x - 3}{2 x ( 5 b x ^{3} - 3 x )}

\int 3 + x d x

\int \frac{2}{4 x ^{2} - 1} d x

\int_{0}^{2} \frac{1}{x ^{2} - x - 2} d x

(x^{3} + 5) e^{x}

\frac{d}{d x} (in y (x))

What is the derivative of ln(5bx^3-3sqrt(x)) ?
The derivative of ln(5bx^3-3sqrt(x)) is (30bx^2sqrt(x)-3)/(2sqrt(x)(5bx^3-3\sqrt{x))}
What is the first derivative of ln(5bx^3-3sqrt(x)) ?
The first derivative of ln(5bx^3-3sqrt(x)) is (30bx^2sqrt(x)-3)/(2sqrt(x)(5bx^3-3\sqrt{x))}