What is the derivative of f(x)=-3x^5cos(x) ?

The derivative of f(x)=-3x^5cos(x) is -3(5x^4cos(x)-x^5sin(x))

What is the first derivative of f(x)=-3x^5cos(x) ?

The first derivative of f(x)=-3x^5cos(x) is -3(5x^4cos(x)-x^5sin(x))

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derivative of

f (x) = - 3 x^{5} cos (x)

- 3 (5 x^{4} cos (x) - x^{5} sin (x))

Solution steps

\frac{d}{d x} (- 3 x^{5} cos (x))

Take the constant out:

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

= - 3 \frac{d}{d x} (x^{5} cos (x))

Apply the Product Rule:

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

f = x^{5}, g = cos (x)

= - 3 (\frac{d}{d x} (x^{5}) cos (x) + \frac{d}{d x} (cos (x)) x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= - 3 (5 x^{4} cos (x) + (- sin (x)) x^{5})

Simplify

= - 3 (5 x^{4} cos (x) - x^{5} sin (x))

\int \frac{x ^{3}}{( 1 + x ^{4} ) ^{\frac{1}{2}}} d x

f (x) = x^{\frac{5}{2}} e^{x}

\int sec^{2} (x) csc (x) d x

\int 3 sin^{2} (x) cos (x) d x

f (x) = \frac{e ^{x}}{x ^{2}}

What is the derivative of f(x)=-3x^5cos(x) ?
The derivative of f(x)=-3x^5cos(x) is -3(5x^4cos(x)-x^5sin(x))
What is the first derivative of f(x)=-3x^5cos(x) ?
The first derivative of f(x)=-3x^5cos(x) is -3(5x^4cos(x)-x^5sin(x))