What is the derivative of f(x)=8x^4tan(x) ?

The derivative of f(x)=8x^4tan(x) is 8(4x^3tan(x)+sec^2(x)x^4)

What is the first derivative of f(x)=8x^4tan(x) ?

The first derivative of f(x)=8x^4tan(x) is 8(4x^3tan(x)+sec^2(x)x^4)

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derivative of

f (x) = 8 x^{4} tan (x)

8 (4 x^{3} tan (x) + sec^{2} (x) x^{4})

Solution steps

\frac{d}{d x} (8 x^{4} tan (x))

Take the constant out:

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

= 8 \frac{d}{d x} (x^{4} tan (x))

Apply the Product Rule:

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

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

= 8 (\frac{d}{d x} (x^{4}) tan (x) + \frac{d}{d x} (tan (x)) x^{4})

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

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

= 8 (4 x^{3} tan (x) + sec^{2} (x) x^{4})

What is the derivative of f(x)=8x^4tan(x) ?
The derivative of f(x)=8x^4tan(x) is 8(4x^3tan(x)+sec^2(x)x^4)
What is the first derivative of f(x)=8x^4tan(x) ?
The first derivative of f(x)=8x^4tan(x) is 8(4x^3tan(x)+sec^2(x)x^4)