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Popular >

derivative of sec(5x^3e^x)

Solution

\frac{d}{d x} (sec (5 x^{3} e^{x}))

Solution

sec (5 x^{3} e^{x}) tan (5 x^{3} e^{x}) \cdot 5 (3 x^{2} e^{x} + e^{x} x^{3})

Solution steps

\frac{d}{d x} (sec (5 x^{3} e^{x}))

Apply the chain rule:

sec (5 x^{3} e^{x}) tan (5 x^{3} e^{x}) \frac{d}{d x} (5 x^{3} e^{x})

= sec (5 x^{3} e^{x}) tan (5 x^{3} e^{x}) \frac{d}{d x} (5 x^{3} e^{x})

\frac{d}{d x} (5 x^{3} e^{x}) = 5 (3 x^{2} e^{x} + e^{x} x^{3})

= sec (5 x^{3} e^{x}) tan (5 x^{3} e^{x}) \cdot 5 (3 x^{2} e^{x} + e^{x} x^{3})

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of sec(5x^3e^x) ?
The derivative of sec(5x^3e^x) is sec(5x^3e^x)tan(5x^3e^x)*5(3x^2e^x+e^xx^3)
What is the first derivative of sec(5x^3e^x) ?
The first derivative of sec(5x^3e^x) is sec(5x^3e^x)tan(5x^3e^x)*5(3x^2e^x+e^xx^3)