What is the derivative of ({f}(x)(x^8)) ?

The derivative of ({f}(x)(x^8)) is derivative of {f}(x)x^8+8x^7{f}(x)

What is the first derivative of ({f}(x)(x^8)) ?

The first derivative of ({f}(x)(x^8)) is derivative of {f}(x)x^8+8x^7{f}(x)

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\frac{d}{d x} ((f (x)) (x^{8}))

\frac{d}{d x} (f (x)) x^{8} + 8 x^{7} f (x)

Solution steps

\frac{d}{d x} ((f (x)) (x^{8}))

Apply the Product Rule:

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

f = f (x), g = x^{8}

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

\frac{d}{d x} (x^{8}) = 8 x^{7}

= \frac{d}{d x} (f (x)) x^{8} + 8 x^{7} f (x)

amnb + nbma - bnma - mbna

216 m^{3} - n^{21} p^{9}

- (x cos (x))

121 + 198 \times 6 + 81 \times 12

What is the derivative of ({f}(x)(x^8)) ?
The derivative of ({f}(x)(x^8)) is derivative of {f}(x)x^8+8x^7{f}(x)
What is the first derivative of ({f}(x)(x^8)) ?
The first derivative of ({f}(x)(x^8)) is derivative of {f}(x)x^8+8x^7{f}(x)