What is the derivative of y=5x^4f(x) ?

The derivative of y=5x^4f(x) is 5(4x^3f(x)+(df)/(dx)x^4)

What is the first derivative of y=5x^4f(x) ?

The first derivative of y=5x^4f(x) is 5(4x^3f(x)+(df)/(dx)x^4)

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derivative of

y = 5 x^{4} f (x)

5 (4 x^{3} f (x) + \frac{df}{d x} x^{4})

Solution steps

\frac{d}{d x} (5 x^{4} f (x))

Take the constant out:

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

= 5 \frac{d}{d x} (x^{4} f (x))

Apply the Product Rule:

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

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

= 5 (\frac{d}{d x} (x^{4}) f (x) + \frac{df}{d x} x^{4})

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

= 5 (4 x^{3} f (x) + \frac{df}{d x} x^{4})

20 y^{^{''}} - y^{^{'}} + 7 y = 0

\frac{d}{d x} (\frac{n}{x})

\frac{d}{d x} (ln ((x + 2)^{3}))

f^{^{'}} (t) - f (t) = - 8 t

\int e^{i 6 x} cos (4 x) d x

What is the derivative of y=5x^4f(x) ?
The derivative of y=5x^4f(x) is 5(4x^3f(x)+(df)/(dx)x^4)
What is the first derivative of y=5x^4f(x) ?
The first derivative of y=5x^4f(x) is 5(4x^3f(x)+(df)/(dx)x^4)