What is (\partial)/(\partial x)(9csc(6x^4-9x+5)) ?

The answer to (\partial)/(\partial x)(9csc(6x^4-9x+5)) is -9cot(6x^4-9x+5)csc(6x^4-9x+5)(24x^3-9)

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(\partial)/(\partial x)(9csc(6x^4-9x+5))

\frac{\partial}{\partial x} (9 csc (6 x^{4} - 9 x + 5))

- 9 cot (6 x^{4} - 9 x + 5) csc (6 x^{4} - 9 x + 5) (24 x^{3} - 9)

Solution steps

\frac{\partial}{\partial x} (9 csc (6 x^{4} - 9 x + 5))

Take the constant out:

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

= 9 \frac{\partial}{\partial x} (csc (6 x^{4} - 9 x + 5))

Apply the chain rule:

- cot (6 x^{4} - 9 x + 5) csc (6 x^{4} - 9 x + 5) \frac{\partial}{\partial x} (6 x^{4} - 9 x + 5)

= - cot (6 x^{4} - 9 x + 5) csc (6 x^{4} - 9 x + 5) \frac{\partial}{\partial x} (6 x^{4} - 9 x + 5)

\frac{\partial}{\partial x} (6 x^{4} - 9 x + 5) = 24 x^{3} - 9

= 9 (- cot (6 x^{4} - 9 x + 5) csc (6 x^{4} - 9 x + 5) (24 x^{3} - 9))

Simplify

= - 9 cot (6 x^{4} - 9 x + 5) csc (6 x^{4} - 9 x + 5) (24 x^{3} - 9)

\frac{d y}{d x}, e^{\frac{x}{y}} = 6 x - y

\frac{d}{d x} (\frac{8}{( 1 - 2 x ) ^{3}})

\frac{d}{d x} (\frac{x ^{5}}{10})

y = 6 - x^{2}, y = 8 - 3 x

x \to \infty lim (4 x + 2)

What is (\partial)/(\partial x)(9csc(6x^4-9x+5)) ?
The answer to (\partial)/(\partial x)(9csc(6x^4-9x+5)) is -9cot(6x^4-9x+5)csc(6x^4-9x+5)(24x^3-9)