What is the derivative of-(3x^2sin((x^3/4))/(4)) ?

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = sin (\frac{x ^{3}}{4})

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

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

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

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

\frac{3 x ^{2} cos ( \frac{x ^{3}}{4} )}{4} x^{2} = \frac{3 x ^{4} cos ( \frac{x ^{3}}{4} )}{4}

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

6 sec (x), at x = \frac{π}{6}

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

x \to - 2 lim (f (x) x)

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

x \to 0 lim (x ln (x + x^{2}))

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