What is the derivative of (sin(3x+1)/(7x^2+1)) ?

The derivative of (sin(3x+1)/(7x^2+1)) is (cos(3x+1)*3(7x^2+1)-14xsin(3x+1))/((7x^2+1)^2)

What is the first derivative of (sin(3x+1)/(7x^2+1)) ?

The first derivative of (sin(3x+1)/(7x^2+1)) is (cos(3x+1)*3(7x^2+1)-14xsin(3x+1))/((7x^2+1)^2)

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\frac{d}{d x} (\frac{sin ( 3 x + 1 )}{7 x ^{2} + 1})

\frac{cos ( 3 x + 1 ) \cdot 3 ( 7 x ^{2} + 1 ) - 14 x sin ( 3 x + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{sin ( 3 x + 1 )}{7 x ^{2} + 1})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( sin ( 3 x + 1 ) ) ( 7 x ^{2} + 1 ) - \frac{d}{d x} ( 7 x ^{2} + 1 ) sin ( 3 x + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (sin (3 x + 1)) = cos (3 x + 1) \cdot 3

\frac{d}{d x} (7 x^{2} + 1) = 14 x

= \frac{cos ( 3 x + 1 ) \cdot 3 ( 7 x ^{2} + 1 ) - 14 x sin ( 3 x + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

\int \frac{12 x}{1 - x ^{4}} d x

f (x) = \frac{x}{x - 2}

\int \frac{1}{3 t - 1} d t

n \to \infty lim (\frac{3 n ^{2} + 7 n + 11}{8 n ^{2} - 5 n + 3})

\int 4 x + 6 d x

What is the derivative of (sin(3x+1)/(7x^2+1)) ?
The derivative of (sin(3x+1)/(7x^2+1)) is (cos(3x+1)*3(7x^2+1)-14xsin(3x+1))/((7x^2+1)^2)
What is the first derivative of (sin(3x+1)/(7x^2+1)) ?
The first derivative of (sin(3x+1)/(7x^2+1)) is (cos(3x+1)*3(7x^2+1)-14xsin(3x+1))/((7x^2+1)^2)