What is the derivative of ln(sqrt(h(x^2))) ?

The derivative of ln(sqrt(h(x^2))) is 1/(|x|)

What is the first derivative of ln(sqrt(h(x^2))) ?

The first derivative of ln(sqrt(h(x^2))) is 1/(|x|)

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\frac{d}{d x} (ln (h (x^{2})))

\frac{1}{∣ x ∣}

Solution steps

\frac{d}{d x} (ln (h (x^{2})))

Simplify

ln (h (x^{2})) : ln (h x^{2})

= \frac{d}{d x} (ln (h x^{2}))

Treat

h

as a constant

Apply the chain rule:

\frac{1}{h x ^{2}} \frac{d}{d x} (h x^{2})

= \frac{1}{h x ^{2}} \frac{d}{d x} (h x^{2})

\frac{d}{d x} (h x^{2}) = \frac{h x}{∣ x ∣}

= \frac{1}{h x ^{2}} \cdot \frac{h x}{∣ x ∣}

Simplify

\frac{1}{h x ^{2}} \cdot \frac{h x}{∣ x ∣} : \frac{1}{∣ x ∣}

= \frac{1}{∣ x ∣}

\int t sin (7 t) d t

\int \frac{2 - x}{x ^{2} + 2 x - 3} d x

\int_{0}^{2} 3 x^{3} x^{2} + 4 d x

x d x + y e^{- x} d y = 0, y^{0} = 1

What is the derivative of ln(sqrt(h(x^2))) ?
The derivative of ln(sqrt(h(x^2))) is 1/(|x|)
What is the first derivative of ln(sqrt(h(x^2))) ?
The first derivative of ln(sqrt(h(x^2))) is 1/(|x|)