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

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

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

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

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

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

Solution steps

\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})

= \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}

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

Simplify

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

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

(1.4) (2.2)

x \to 0 lim (\frac{∣ x - 2 ∣}{x - 2})

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

1 0^{5 x^{2} - 3 x}

\int_{1}^{\infty} e^{- x^{2}} d x

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