What is the derivative of sin(ln(3x^2+x)) ?

The derivative of sin(ln(3x^2+x)) is (cos(ln(3x^2+x))(6x+1))/(3x^2+x)

What is the first derivative of sin(ln(3x^2+x)) ?

The first derivative of sin(ln(3x^2+x)) is (cos(ln(3x^2+x))(6x+1))/(3x^2+x)

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\frac{d}{d x} (sin (ln (3 x^{2} + x)))

\frac{cos ( ln ( 3 x ^{2} + x ) ) ( 6 x + 1 )}{3 x ^{2} + x}

Solution steps

\frac{d}{d x} (sin (ln (3 x^{2} + x)))

Apply the chain rule:

cos (ln (3 x^{2} + x)) \frac{d}{d x} (ln (3 x^{2} + x))

= cos (ln (3 x^{2} + x)) \frac{d}{d x} (ln (3 x^{2} + x))

\frac{d}{d x} (ln (3 x^{2} + x)) = \frac{6 x + 1}{3 x ^{2} + x}

= cos (ln (3 x^{2} + x)) \frac{6 x + 1}{3 x ^{2} + x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{cos ( ln ( 3 x ^{2} + x ) ) ( 6 x + 1 )}{3 x ^{2} + x}

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

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

\frac{d}{d x} (a x e^{2 x})

f (x) = x^{3} + x^{2} + (\frac{6}{x}), at x = 1

y = (x - 4)^{2}, at x = 5

What is the derivative of sin(ln(3x^2+x)) ?
The derivative of sin(ln(3x^2+x)) is (cos(ln(3x^2+x))(6x+1))/(3x^2+x)
What is the first derivative of sin(ln(3x^2+x)) ?
The first derivative of sin(ln(3x^2+x)) is (cos(ln(3x^2+x))(6x+1))/(3x^2+x)