What is the derivative of 7csc(x^5) ?

The derivative of 7csc(x^5) is -35x^4cot(x^5)csc(x^5)

What is the first derivative of 7csc(x^5) ?

The first derivative of 7csc(x^5) is -35x^4cot(x^5)csc(x^5)

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\frac{d}{d x} (7 csc (x^{5}))

- 35 x^{4} cot (x^{5}) csc (x^{5})

Solution steps

\frac{d}{d x} (7 csc (x^{5}))

Take the constant out:

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

= 7 \frac{d}{d x} (csc (x^{5}))

Apply the chain rule:

- cot (x^{5}) csc (x^{5}) \frac{d}{d x} (x^{5})

= - cot (x^{5}) csc (x^{5}) \frac{d}{d x} (x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

= 7 (- cot (x^{5}) csc (x^{5}) \cdot 5 x^{4})

Simplify

= - 35 x^{4} cot (x^{5}) csc (x^{5})

x \to - 4 lim (4 + x)

y^{^{''}} + y = \frac{1}{4} cos (3 t)

\int_{1}^{4} 16 x^{5} d x

\frac{d y}{d x} = - 2 x (y - 3)

What is the derivative of 7csc(x^5) ?
The derivative of 7csc(x^5) is -35x^4cot(x^5)csc(x^5)
What is the first derivative of 7csc(x^5) ?
The first derivative of 7csc(x^5) is -35x^4cot(x^5)csc(x^5)