What is the derivative of sin^4(2xcos^43x) ?

The derivative of sin^4(2xcos^43x) is 3s^4(8cxosin^3(2cxo)cos(2cxo)+sin^4(2cxo))

What is the first derivative of sin^4(2xcos^43x) ?

The first derivative of sin^4(2xcos^43x) is 3s^4(8cxosin^3(2cxo)cos(2cxo)+sin^4(2cxo))

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\frac{d}{d x} (sin^{4} (2 x co) s^{4} 3 x)

3 s^{4} (8 c x o sin^{3} (2 c x o) cos (2 c x o) + sin^{4} (2 c x o))

Solution steps

\frac{d}{d x} (sin^{4} (2 x co) s^{4} \cdot 3 x)

Treat

c, s, o

as a constant

Take the constant out:

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

= s^{4} \cdot 3 \frac{d}{d x} (sin^{4} (2 x co) x)

Apply the Product Rule:

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

f = sin^{4} (2 x co), g = x

= s^{4} \cdot 3 (\frac{d}{d x} (sin^{4} (2 x co)) x + \frac{d x}{d x} sin^{4} (2 x co))

\frac{d}{d x} (sin^{4} (2 x co)) = 8 co sin^{3} (2 co x) cos (2 co x)

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

= s^{4} \cdot 3 (8 co sin^{3} (2 co x) cos (2 co x) x + 1 \cdot sin^{4} (2 x co))

Simplify

= 3 s^{4} (8 c x o sin^{3} (2 c x o) cos (2 c x o) + sin^{4} (2 c x o))

What is the derivative of sin^4(2xcos^43x) ?
The derivative of sin^4(2xcos^43x) is 3s^4(8cxosin^3(2cxo)cos(2cxo)+sin^4(2cxo))
What is the first derivative of sin^4(2xcos^43x) ?
The first derivative of sin^4(2xcos^43x) is 3s^4(8cxosin^3(2cxo)cos(2cxo)+sin^4(2cxo))