What is the derivative of x^4(tan(x+sec(x))) ?

The derivative of x^4(tan(x+sec(x))) is 4x^3(tan(x)+sec(x))-(x^4)/(-1+sin(x))

What is the first derivative of x^4(tan(x+sec(x))) ?

The first derivative of x^4(tan(x+sec(x))) is 4x^3(tan(x)+sec(x))-(x^4)/(-1+sin(x))

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\frac{d}{d x} (x^{4} (tan (x) + sec (x)))

4 x^{3} (tan (x) + sec (x)) - \frac{x ^{4}}{- 1 + sin ( x )}

Solution steps

\frac{d}{d x} (x^{4} (tan (x) + sec (x)))

Apply the Product Rule:

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

f = x^{4}, g = tan (x) + sec (x)

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

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

\frac{d}{d x} (tan (x) + sec (x)) = - \frac{1}{- 1 + sin ( x )}

= 4 x^{3} (tan (x) + sec (x)) + (- \frac{1}{- 1 + sin ( x )}) x^{4}

Simplify

4 x^{3} (tan (x) + sec (x)) + (- \frac{1}{- 1 + sin ( x )}) x^{4} : 4 x^{3} (tan (x) + sec (x)) - \frac{x ^{4}}{- 1 + sin ( x )}

= 4 x^{3} (tan (x) + sec (x)) - \frac{x ^{4}}{- 1 + sin ( x )}

x \to 0 lim (- x^{2} + 5 x + a)

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

\frac{d}{d t} (t^{2} (3 - t)^{3})

\frac{\partial}{\partial x} (tan (\frac{x}{y}))

y^{^{''}} + 9 y = sec^{2} (3 t)

What is the derivative of x^4(tan(x+sec(x))) ?
The derivative of x^4(tan(x+sec(x))) is 4x^3(tan(x)+sec(x))-(x^4)/(-1+sin(x))
What is the first derivative of x^4(tan(x+sec(x))) ?
The first derivative of x^4(tan(x+sec(x))) is 4x^3(tan(x)+sec(x))-(x^4)/(-1+sin(x))