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Popular Calculus >

derivative of 4x^3sec(7x)

Solution

\frac{d}{d x} (4 x^{3} sec (7 x))

Solution

4 (3 x^{2} sec (7 x) + sec (7 x) tan (7 x) \cdot 7 x^{3})

Solution steps

\frac{d}{d x} (4 x^{3} sec (7 x))

Take the constant out:

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

= 4 \frac{d}{d x} (x^{3} sec (7 x))

Apply the Product Rule:

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

f = x^{3}, g = sec (7 x)

= 4 (\frac{d}{d x} (x^{3}) sec (7 x) + \frac{d}{d x} (sec (7 x)) x^{3})

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

\frac{d}{d x} (sec (7 x)) = sec (7 x) tan (7 x) \cdot 7

= 4 (3 x^{2} sec (7 x) + sec (7 x) tan (7 x) \cdot 7 x^{3})

Graph

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y^{''}+4y^'+5y=15x+e^{-x}

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Frequently Asked Questions (FAQ)

What is the derivative of 4x^3sec(7x) ?
The derivative of 4x^3sec(7x) is 4(3x^2sec(7x)+sec(7x)tan(7x)*7x^3)
What is the first derivative of 4x^3sec(7x) ?
The first derivative of 4x^3sec(7x) is 4(3x^2sec(7x)+sec(7x)tan(7x)*7x^3)