What is the derivative of (3x^4+3/(sin(x))) ?

The derivative of (3x^4+3/(sin(x))) is (12x^3sin(x)-cos(x)(3x^4+3))/(sin^2(x))

What is the first derivative of (3x^4+3/(sin(x))) ?

The first derivative of (3x^4+3/(sin(x))) is (12x^3sin(x)-cos(x)(3x^4+3))/(sin^2(x))

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\frac{d}{d x} (\frac{3 x ^{4} + 3}{sin ( x )})

\frac{12 x ^{3} sin ( x ) - cos ( x ) ( 3 x ^{4} + 3 )}{sin ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{3 x ^{4} + 3}{sin ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x ^{4} + 3 ) sin ( x ) - \frac{d}{d x} ( sin ( x ) ) ( 3 x ^{4} + 3 )}{( sin ( x ) ) ^{2}}

\frac{d}{d x} (3 x^{4} + 3) = 12 x^{3}

\frac{d}{d x} (sin (x)) = cos (x)

= \frac{12 x ^{3} sin ( x ) - cos ( x ) ( 3 x ^{4} + 3 )}{( sin ( x ) ) ^{2}}

Simplify

= \frac{12 x ^{3} sin ( x ) - cos ( x ) ( 3 x ^{4} + 3 )}{sin ^{2} ( x )}

\frac{d}{d s} (s^{2} + t^{2})

3 x^{4} - 7 x^{2}, at x = - 1

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

\frac{d y}{d x} = 4 y^{2} sec^{2} (2 x), y (\frac{π}{8}) = 1

x \to - 3 lim (\frac{1}{2} - x^{3})

What is the derivative of (3x^4+3/(sin(x))) ?
The derivative of (3x^4+3/(sin(x))) is (12x^3sin(x)-cos(x)(3x^4+3))/(sin^2(x))
What is the first derivative of (3x^4+3/(sin(x))) ?
The first derivative of (3x^4+3/(sin(x))) is (12x^3sin(x)-cos(x)(3x^4+3))/(sin^2(x))