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Find the derivative of the function. G(Z) - (1 - 32) V 23 + 1 Differentiate. G' ( Z) = h(0) = 02 sin(0) Bb Web Assign fall 2021 - Calculus 1 (51) MATH We first note that we can rewrite the function as follows. f(x) = x3 ( x+ 9) h'(0) = = x4 + 9x3 Step 2 We have rewritten the given function as f(x) = x4 + 9x3, and we wish to find the de Differentiate. words, we need to find the following. f' ( x) = - (x4 + 9x3) Recall the sum rule, which states that if g and h are both differentiable, then the foll y = sec(0) tan(0) dx 9 ( x ) + h(x) = gl dy 9 ( x ) + - h ( x ) Applying this rule allows us to rewrite as follows. f' ( x ) = - (x4 + 9x3 ) X d 4 dx (9x 3 ) Step 3 Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] (Use non-identity functions for f(u) and g(x).) Recall the constant multiple rule, where c is a constant and g is a differentiable function y = V x5 + 8 cg ( x) = c d g ( x (f (u ), g ( x ) ) = ( Applying this rule to the second of our two derivative gives us the following. ( x 4 ) + (9x 3 ) = 6 ( x 4 ) + ( Find the derivative - dy dx dy Submit Skip (you cannot come back) dx