What is the derivative of f(x)=6cos^4(3x+2) ?

The derivative of f(x)=6cos^4(3x+2) is -72cos^3(3x+2)sin(3x+2)

What is the first derivative of f(x)=6cos^4(3x+2) ?

The first derivative of f(x)=6cos^4(3x+2) is -72cos^3(3x+2)sin(3x+2)

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derivative of

f (x) = 6 cos^{4} (3 x + 2)

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

Solution steps

\frac{d}{d x} (6 cos^{4} (3 x + 2))

Take the constant out:

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

= 6 \frac{d}{d x} (cos^{4} (3 x + 2))

Apply the chain rule:

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

= 4 (cos (3 x + 2))^{3} \frac{d}{d x} (cos (3 x + 2))

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

= 6 \cdot 4 (cos (3 x + 2))^{3} (- sin (3 x + 2) \cdot 3)

Simplify

= - 72 cos^{3} (3 x + 2) sin (3 x + 2)

x \to 5 lim (x^{3} - x^{2} + 5 x)

y^{^{'}} = y tan (t) + sin (t)

\frac{d}{d x} ((\frac{1}{x} - \frac{4}{x ^{3}}) (x^{3} - 5 x - 1))

x \to 1 lim (x^{5} - 2 x - 6)

\frac{d}{d x} (\frac{csc ( x )}{1 + csc ( x )})

What is the derivative of f(x)=6cos^4(3x+2) ?
The derivative of f(x)=6cos^4(3x+2) is -72cos^3(3x+2)sin(3x+2)
What is the first derivative of f(x)=6cos^4(3x+2) ?
The first derivative of f(x)=6cos^4(3x+2) is -72cos^3(3x+2)sin(3x+2)