What is the derivative of e^{4x^2}csc(5x) ?

The derivative of e^{4x^2}csc(5x) is 8e^{4x^2}xcsc(5x)-5e^{4x^2}cot(5x)csc(5x)

What is the first derivative of e^{4x^2}csc(5x) ?

The first derivative of e^{4x^2}csc(5x) is 8e^{4x^2}xcsc(5x)-5e^{4x^2}cot(5x)csc(5x)

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\frac{d}{d x} (e^{4 x^{2}} csc (5 x))

8 e^{4 x^{2}} x csc (5 x) - 5 e^{4 x^{2}} cot (5 x) csc (5 x)

Solution steps

\frac{d}{d x} (e^{4 x^{2}} csc (5 x))

Apply the Product Rule:

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

f = e^{4 x^{2}}, g = csc (5 x)

= \frac{d}{d x} (e^{4 x^{2}}) csc (5 x) + \frac{d}{d x} (csc (5 x)) e^{4 x^{2}}

\frac{d}{d x} (e^{4 x^{2}}) = e^{4 x^{2}} \cdot 8 x

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

= e^{4 x^{2}} \cdot 8 x csc (5 x) + (- cot (5 x) csc (5 x) \cdot 5) e^{4 x^{2}}

Simplify

= 8 e^{4 x^{2}} x csc (5 x) - 5 e^{4 x^{2}} cot (5 x) csc (5 x)

sin (- 2 x)

\int \frac{1}{10 ( x ^{2} + 1 )} d x

(2 x - 7)^{- 1} (x + 5)

\frac{d}{d x} (- 4 cot (x))

(1 + x^{2})^{^{'}}

What is the derivative of e^{4x^2}csc(5x) ?
The derivative of e^{4x^2}csc(5x) is 8e^{4x^2}xcsc(5x)-5e^{4x^2}cot(5x)csc(5x)
What is the first derivative of e^{4x^2}csc(5x) ?
The first derivative of e^{4x^2}csc(5x) is 8e^{4x^2}xcsc(5x)-5e^{4x^2}cot(5x)csc(5x)