What is the derivative of cos^3(x3x(cos(x))^') ?

The derivative of cos^3(x3x(cos(x))^') is 3(cos^{3+'}(x)-(3+')xtan(x)cos^{3+'}(x))

What is the first derivative of cos^3(x3x(cos(x))^') ?

The first derivative of cos^3(x3x(cos(x))^') is 3(cos^{3+'}(x)-(3+')xtan(x)cos^{3+'}(x))

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

3 (cos^{3 +'} (x) - (3 +') x tan (x) cos^{3 +'} (x))

Solution steps

\frac{d}{d x} (cos^{3} (x) \cdot 3 x (cos (x))^{^{'}})

Simplify

cos^{3} (x) \cdot 3 x (cos (x))^{^{'}} : 3 x cos^{3 +^{'}} (x)

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 3 (1 \cdot cos^{3 +^{^{'}}} (x) + (- (3 +^{^{'}}) tan (x) cos^{3 +^{^{'}}} (x)) x)

Simplify

= 3 (cos^{3 +^{^{'}}} (x) - (3 +^{^{'}}) x tan (x) cos^{3 +^{^{'}}} (x))

3 tan^{3} (x)

cos^{2} (5 x)

\frac{1 - t ^{2}}{4}

\frac{d}{d s} (\frac{( 13 ( s + 2 ) ( s + 5 ) )}{( s ( s + 3 ) )})

q (t) = 6 t^{2} + 5 t + 4

What is the derivative of cos^3(x3x(cos(x))^') ?
The derivative of cos^3(x3x(cos(x))^') is 3(cos^{3+'}(x)-(3+')xtan(x)cos^{3+'}(x))
What is the first derivative of cos^3(x3x(cos(x))^') ?
The first derivative of cos^3(x3x(cos(x))^') is 3(cos^{3+'}(x)-(3+')xtan(x)cos^{3+'}(x))