What is the derivative of-7csc(5x)e^{3x} ?

The derivative of-7csc(5x)e^{3x} is -7(-5e^{3x}cot(5x)csc(5x)+3e^{3x}csc(5x))

What is the first derivative of-7csc(5x)e^{3x} ?

The first derivative of-7csc(5x)e^{3x} is -7(-5e^{3x}cot(5x)csc(5x)+3e^{3x}csc(5x))

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derivative of

- 7 csc (5 x) e^{3 x}

- 7 (- 5 e^{3 x} cot (5 x) csc (5 x) + 3 e^{3 x} csc (5 x))

Solution steps

\frac{d}{d x} (- 7 csc (5 x) e^{3 x})

Take the constant out:

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

= - 7 \frac{d}{d x} (csc (5 x) e^{3 x})

Apply the Product Rule:

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

f = csc (5 x), g = e^{3 x}

= - 7 (\frac{d}{d x} (csc (5 x)) e^{3 x} + \frac{d}{d x} (e^{3 x}) csc (5 x))

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

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

= - 7 ((- cot (5 x) csc (5 x) \cdot 5) e^{3 x} + e^{3 x} \cdot 3 csc (5 x))

Simplify

= - 7 (- 5 e^{3 x} cot (5 x) csc (5 x) + 3 e^{3 x} csc (5 x))

What is the derivative of-7csc(5x)e^{3x} ?
The derivative of-7csc(5x)e^{3x} is -7(-5e^{3x}cot(5x)csc(5x)+3e^{3x}csc(5x))
What is the first derivative of-7csc(5x)e^{3x} ?
The first derivative of-7csc(5x)e^{3x} is -7(-5e^{3x}cot(5x)csc(5x)+3e^{3x}csc(5x))