What is the derivative of 3x^2cos(x^3) ?

The derivative of 3x^2cos(x^3) is 3(2xcos(x^3)-3x^4sin(x^3))

What is the first derivative of 3x^2cos(x^3) ?

The first derivative of 3x^2cos(x^3) is 3(2xcos(x^3)-3x^4sin(x^3))

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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