What is the derivative of f(x)=sin^5(3x^2-x+13) ?

The derivative of f(x)=sin^5(3x^2-x+13) is 5sin^4(3x^2-x+13)cos(3x^2-x+13)(6x-1)

What is the first derivative of f(x)=sin^5(3x^2-x+13) ?

The first derivative of f(x)=sin^5(3x^2-x+13) is 5sin^4(3x^2-x+13)cos(3x^2-x+13)(6x-1)

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derivative of

f (x) = sin^{5} (3 x^{2} - x + 13)

5 sin^{4} (3 x^{2} - x + 13) cos (3 x^{2} - x + 13) (6 x - 1)

Solution steps

\frac{d}{d x} (sin^{5} (3 x^{2} - x + 13))

Apply the chain rule:

5 (sin (3 x^{2} - x + 13))^{4} \frac{d}{d x} (sin (3 x^{2} - x + 13))

= 5 (sin (3 x^{2} - x + 13))^{4} \frac{d}{d x} (sin (3 x^{2} - x + 13))

\frac{d}{d x} (sin (3 x^{2} - x + 13)) = cos (3 x^{2} - x + 13) (6 x - 1)

= 5 (sin (3 x^{2} - x + 13))^{4} cos (3 x^{2} - x + 13) (6 x - 1)

Simplify

= 5 sin^{4} (3 x^{2} - x + 13) cos (3 x^{2} - x + 13) (6 x - 1)

\frac{81}{( 6 ( \frac{1}{6} ) + 8 ) ^{\frac{5}{2}}}

(arctan (5 x))^{2}

\frac{d}{d x} (x - 2 + y - 1)

x \to 1 + lim (\frac{x + 10}{1 - x})

x^{2} + x y + y^{2} = 3, (1, 1)

What is the derivative of f(x)=sin^5(3x^2-x+13) ?
The derivative of f(x)=sin^5(3x^2-x+13) is 5sin^4(3x^2-x+13)cos(3x^2-x+13)(6x-1)
What is the first derivative of f(x)=sin^5(3x^2-x+13) ?
The first derivative of f(x)=sin^5(3x^2-x+13) is 5sin^4(3x^2-x+13)cos(3x^2-x+13)(6x-1)