What is the derivative of 6x^3cos(x) ?

The derivative of 6x^3cos(x) is 6(3x^2cos(x)-x^3sin(x))

What is the first derivative of 6x^3cos(x) ?

The first derivative of 6x^3cos(x) is 6(3x^2cos(x)-x^3sin(x))

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\frac{d}{d x} (6 x^{3} cos (x))

6 (3 x^{2} cos (x) - x^{3} sin (x))

Solution steps

\frac{d}{d x} (6 x^{3} cos (x))

Take the constant out:

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

= 6 \frac{d}{d x} (x^{3} cos (x))

Apply the Product Rule:

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

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

= 6 (\frac{d}{d x} (x^{3}) cos (x) + \frac{d}{d x} (cos (x)) x^{3})

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

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

= 6 (3 x^{2} cos (x) + (- sin (x)) x^{3})

Simplify

= 6 (3 x^{2} cos (x) - x^{3} sin (x))

4 x y^{^{'}} + 2 y = 10 x^{6}

\int \frac{x ^{3} + x ^{2}}{x ^{5}} d x

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

13 x

\int \frac{2 x}{e ^{8 x}} d x

What is the derivative of 6x^3cos(x) ?
The derivative of 6x^3cos(x) is 6(3x^2cos(x)-x^3sin(x))
What is the first derivative of 6x^3cos(x) ?
The first derivative of 6x^3cos(x) is 6(3x^2cos(x)-x^3sin(x))