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Popular >

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})

Popular Examples

(x^2+1)y^'+7x(y-1)=0

(x^{2} + 1) y^{^{'}} + 7 x (y - 1) = 0

(x-2)y^'-y=2(x-2)^3,y(3)=5

(x - 2) y^{^{'}} - y = 2 (x - 2)^{3}, y (3) = 5

integral of (2xln(x^2+1))/(x^2+1)

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

tangent of sqrt(x^2+16),\at x=3 tangent of

x^{2} + 16, at x = 3

integral of 1/3 x^3sqrt(9-x^2)

\int \frac{1}{3} x^{3} 9 - x^{2} d x

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)