What is the derivative of sin^3(3x^7-2x+i) ?

The derivative of sin^3(3x^7-2x+i) is 3sin^2(3x^7-2x+i)cos(3x^7-2x+i)(21x^6-2)

What is the first derivative of sin^3(3x^7-2x+i) ?

The first derivative of sin^3(3x^7-2x+i) is 3sin^2(3x^7-2x+i)cos(3x^7-2x+i)(21x^6-2)

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\frac{d}{d x} (sin^{3} (3 x^{7} - 2 x + i))

3 sin^{2} (3 x^{7} - 2 x + i) cos (3 x^{7} - 2 x + i) (21 x^{6} - 2)

Solution steps

\frac{d}{d x} (sin^{3} (3 x^{7} - 2 x + i))

Apply the chain rule:

3 (sin (3 x^{7} - 2 x + i))^{2} \frac{d}{d x} (sin (3 x^{7} - 2 x + i))

= 3 (sin (3 x^{7} - 2 x + i))^{2} \frac{d}{d x} (sin (3 x^{7} - 2 x + i))

\frac{d}{d x} (sin (3 x^{7} - 2 x + i)) = cos (3 x^{7} - 2 x + i) (21 x^{6} - 2)

= 3 (sin (3 x^{7} - 2 x + i))^{2} cos (3 x^{7} - 2 x + i) (21 x^{6} - 2)

Simplify

= 3 sin^{2} (3 x^{7} - 2 x + i) cos (3 x^{7} - 2 x + i) (21 x^{6} - 2)

\frac{2 x}{( x ^{2} + 1 )}

y = (x^{4} + 5 x^{2})^{7}

y - x^{2} + 1

6 x^{2} - 1

y = \frac{x + 1}{( x + 2 ) ^{2}}

What is the derivative of sin^3(3x^7-2x+i) ?
The derivative of sin^3(3x^7-2x+i) is 3sin^2(3x^7-2x+i)cos(3x^7-2x+i)(21x^6-2)
What is the first derivative of sin^3(3x^7-2x+i) ?
The first derivative of sin^3(3x^7-2x+i) is 3sin^2(3x^7-2x+i)cos(3x^7-2x+i)(21x^6-2)