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Popular >

derivative of 6cos^4(3x+2)

Solution

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

Solution

- 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)

Popular Examples

inverse oflaplace x^2+1 inverse laplace

x^{2} + 1

y^{''}-3y^'+2y=0,y(0)=1,y^'(0)=-1

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

(d^2y)/(dx^2)-5(dy)/(dx)+6y=5e^{3x}

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = 5 e^{3 x}

inverse oflaplace ((10s-3))/(s^2+4s+29)inverse laplace

\frac{( 10 s - 3 )}{s ^{2} + 4 s + 29}

integral of x/((1+4x^2)^2)

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

Frequently Asked Questions (FAQ)

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