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Popular >

derivative of (x+z(x-5)^8)

Solution

\frac{d}{d x} ((x + z) (x - 5)^{8})

Solution

(1 + \frac{d z}{d x}) (x - 5)^{8} + 8 (x - 5)^{7} (x + z)

Solution steps

\frac{d}{d x} ((x + z) (x - 5)^{8})

Apply the Product Rule:

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

f = x + z, g = (x - 5)^{8}

= \frac{d}{d x} (x + z) (x - 5)^{8} + \frac{d}{d x} ((x - 5)^{8}) (x + z)

\frac{d}{d x} (x + z) = 1 + \frac{d z}{d x}

\frac{d}{d x} ((x - 5)^{8}) = 8 (x - 5)^{7}

= (1 + \frac{d z}{d x}) (x - 5)^{8} + 8 (x - 5)^{7} (x + z)

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Frequently Asked Questions (FAQ)

What is the derivative of (x+z(x-5)^8) ?
The derivative of (x+z(x-5)^8) is (1+(dz)/(dx))(x-5)^8+8(x-5)^7(x+z)
What is the first derivative of (x+z(x-5)^8) ?
The first derivative of (x+z(x-5)^8) is (1+(dz)/(dx))(x-5)^8+8(x-5)^7(x+z)