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Popular >

derivative of x^4sin(xtan(x))

Solution

\frac{d}{d x} (x^{4} sin (x) tan (x))

Solution

4 x^{3} sin (x) tan (x) + sin (x) (1 + sec^{2} (x)) x^{4}

Solution steps

\frac{d}{d x} (x^{4} sin (x) tan (x))

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (sin (x) tan (x)) = sin (x) (1 + sec^{2} (x))

= 4 x^{3} sin (x) tan (x) + sin (x) (1 + sec^{2} (x)) x^{4}

Popular Examples

tangent of-4x^2+7x tangent of

- 4 x^{2} + 7 x

sum from n=3 to infinity of e^{5-4n}

n = 3 \sum \infty e^{5 - 4 n}

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

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

limit as x approaches-3 of (3-|x|)/(x+3)

x \to - 3 lim (\frac{3 - ∣ x ∣}{x + 3})

y^{''}+17y^'+70y=0

y^{^{''}} + 17 y^{^{'}} + 70 y = 0

Frequently Asked Questions (FAQ)

What is the derivative of x^4sin(xtan(x)) ?
The derivative of x^4sin(xtan(x)) is 4x^3sin(x)tan(x)+sin(x)(1+sec^2(x))x^4
What is the first derivative of x^4sin(xtan(x)) ?
The first derivative of x^4sin(xtan(x)) is 4x^3sin(x)tan(x)+sin(x)(1+sec^2(x))x^4