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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

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

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

\int y cos (x y) d x

\int_{2}^{x} \frac{2 x - 3}{6} d x

\frac{d}{d x} (3 sec^{2} (x))

\frac{d y}{d x} = cos (5 x)

tan (u)

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