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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{sin ^{2} ( ln ( x ^{3} ) ) + 1} \cdot \frac{3 cos ( ln ( x ^{3} ) )}{x} : \frac{3 cos ( 3 ln ( x ) )}{x ( sin ^{2} ( 3 ln ( x ) ) + 1 )}

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

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

s l o p e y = 2 x^{3} - x^{2} + 3

\frac{d y}{d x} = 4 x y

\int \frac{1}{1 + 5 x ^{2}} d x

d er i v a t i v e 3 - 5 x

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